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On the usefulness of set-membership estimation in the epidemiology of infectious diseases
An exact approach to calibrating infectious disease models to surveillance data: The case of HIV and HSV-2
Department of Mathematics, Xavier University, 3800 Victory Parkway, Cincinnati, OH 45207, USA |
When mathematical models of infectious diseases are used to inform health policy, an important first step is often to calibrate a model to disease surveillance data for a specific setting (or multiple settings). It is increasingly common to also perform sensitivity analyses to demonstrate the robustness, or lack thereof, of the modeling results. Doing so requires the modeler to find multiple parameter sets for which the model produces behavior that is consistent with the surveillance data. While frequently overlooked, the calibration process is nontrivial at best and can be inefficient, poorly communicated and a major hurdle to the overall reproducibility of modeling results.
In this work, we describe a general approach to calibrating infectious disease models to surveillance data. The technique is able to match surveillance data to high accuracy in a very efficient manner as it is based on the Newton-Raphson method for solving nonlinear systems. To demonstrate its robustness, we use the calibration technique on multiple models for the interacting dynamics of HIV and HSV-2.
References:
[1] |
L. J. Abu-Raddad, A. S. Magaret, C. Celum, A. Wald, I. M. Longini, S. G. Self and L. Corey, Genital herpes has played a more important role than any other sexually transmitted infection in driving hiv prevalence in africa,
PLoS ONE, 3 (2008), e2230. |
[2] |
B. Auvert, R. Ballard, C. Campbell, M. Caraël, M. Carton, G. Fehler, E. Gouws, C. MacPhail, D. Taljaard, J. V. Dam and B. Williams,
Hiv infection among youth in a south african mining town is associated with herpes simplex virus-2 seropositivity and sexual behaviour, AIDS, 15 (2001), 885-898.
|
[3] |
J. M. Baeten, D. Donnell, P. Ndase, N. R. Mugo, J. D. Campbell, J. Wangisi, J. W. Tappero, E. A. Bukusi, C. R. Cohen, E. Katabira, A. Ronald, E. Tumwesigye, E. Were, K. H. Fife, J. Kiarie, C. Farquhar, G. John-Stewart, A. Kakia, J. Odoyo, A. Mucunguzi, E. Nakku-Joloba, R. Twesigye, K. Ngure, C. Apaka, H. Tamooh, F. Gabona, A. Mujugira, D. Panteleeff, K. K. Thomas, L. Kidoguchi, M. Krows, J. Revall, S. Morrison, H. Haugen, M. Emmanuel-Ogier, L. Ondrejcek, R. W. Coombs, L. Frenkel, C. Hendrix, N. N. Bumpus, D. Bangsberg, J. E. Haberer, W. S. Stevens, J. R. Lingappa and C. Celum,
Antiretroviral prophylaxis for HIV prevention in heterosexual men and women, N Engl J Med, 367 (2012), 399-410.
|
[4] |
R. V. Barnabas, E. L. Webb, H. A. Weiss and J. N. Wasserheit,
The role of coinfections in HIV epidemic trajectory and positive prevention, AIDS, 25 (2011), 1559-1573.
|
[5] |
M.-C. Boily, R. F. Baggaley, L. Wang, B. Masse, R. G. White, R. J. Hayes and M. Alary, Heterosexual risk of hiv-1 infection per sexual act: Systematic review and meta-analysis of observational studies, Lancet Infect Dis, 9 (2009), 118–129, URL http://linkinghub.elsevier.com/retrieve/pii/S1473-3099(09)70021-0. |
[6] |
R. Burden and J. Faires,
Numerical Analysis, Cengage Learning, 2010. |
[7] |
Cohen, Chen, McCauley, Gamble, Hosseinipour, Kumarasamy, Hakim, Kumwenda, Grinsztejn, Pilotto, Godbole, Mehendale, Chariyalertsak, Santos, Mayer, Hoffman, Eshleman, Piwowar-Manning, Wang, Makhema, Mills, de Bruyn, Sanne, Eron, Gallant, Havlir, Swindells, Ribaudo, Elharrar, Burns, Taha, Nielsen-Saines, Celentano, Essex, Fleming and HPTN 052 Study Team,
Prevention of HIV-1 infection with early antiretroviral therapy., N Engl J Med, 365 (2011), 493-505.
|
[8] |
M. Das, P. L. Chu, G. -M. Santos, S. Scheer, E. Vittinghoff, W. McFarland and G. N. Colfax, Decreases in community viral load are accompanied by reductions in new HIV infections in san francisco,
PLoS ONE, 5 (2010), e11068. |
[9] |
E. E. Freeman, H. A. Weiss, J. R. Glynn, P. L. Cross, J. A. Whitworth and R. J. Hayes,
Herpes simplex virus 2 infection increases hiv acquisition in men and women: Systematic review and meta-analysis of longitudinal studies, AIDS, 20 (2006), 73-83.
|
[10] |
D. Gerberry, B. G. Wagner, J. G. García-Lerma, W. Heneine and S. Blower,
Using geospatial modelling to optimize the rollout of antiretroviral-based pre-exposure HIV interventions in Sub-Saharan Africa, Nature Communications, 5 (2014), 1-15.
|
[11] |
R. M. Granich, C. F. Gilks, C. Dye, K. M. De Cock and B. G. Williams,
Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: A mathematical model, Lancet, 373 (2009), 48-57.
|
[12] |
R. H. Gray, M. J. Wawer, R. Brookmeyer, N. K. Sewankambo, D. Serwadda, F. Wabwire-Mangen, T. Lutalo, X. Li, T. vanCott, T. C. Quinn and R. P. Team,
Probability of hiv-1 transmission per coital act in monogamous, heterosexual, hiv-1-discordant couples in rakai, uganda, Lancet, 357 (2001), 1149-1153.
|
[13] |
R. J. Hayes, K. F. Schulz and F. A. Plummer,
The cofactor effect of genital ulcers on the per-exposure risk of hiv transmission in sub-saharan africa, J Trop Med Hyg, 98 (1995), 1-8.
|
[14] |
K. A. Powers, C. Poole, A. E. Pettifor and M. S. Cohen,
Rethinking the heterosexual infectivity of hiv-1: A systematic review and meta-analysis, Lancet Infect Dis, 8 (2008), 553-563.
doi: 10.1016/S1473-3099(08)70156-7. |
[15] |
J. A. Røttingen, D. W. Cameron and G. P. Garnett,
A systematic review of the epidemiologic interactions between classic sexually transmitted diseases and hiv: How much really is known?, Sex Transm Dis, 28 (2001), 579-597.
|
[16] |
J. S. Smith and N. J. Robinson,
Age-specific prevalence of infection with herpes simplex virus types 2 and 1: A global review, J Infect Dis, 186 (2002), 3-28.
|
[17] |
R. J. Smith and S. M. Blower,
Could disease-modifying HIV vaccines cause population-level perversity?, Lancet Infect Dis, 4 (2004), 636-639.
doi: 10.1016/S1473-3099(04)01148-X. |
[18] |
The World Bank, World development indicators, http://data.worldbank.org/data--catalog/world--development--indicators [Accessed: 25 Oct 2011], URL http://data.worldbank.org/data-catalog/world-development-indicators. |
[19] |
M. C. Thigpen, P. M. Kebaabetswe, L. A. Paxton, D. K. Smith, C. E. Rose, T. M. Segolodi, F. L. Henderson, S. R. Pathak, F. A. Soud, K. L. Chillag, R. Mutanhaurwa, L. I. Chirwa, M. Kasonde, D. Abebe, E. Buliva, R. J. Gvetadze, S. Johnson, T. Sukalac, V. T. Thomas, C. Hart, J. A. Johnson, C. K. Malotte, C. W. Hendrix and J. T. Brooks,
Antiretroviral preexposure prophylaxis for heterosexual HIV transmission in botswana, N Engl J Med, 367 (2012), 423-434.
doi: 10.1056/NEJMoa1110711. |
[20] |
A. J. Vyse, N. J. Gay, M. J. Slomka, R. Gopal, T. Gibbs, P. Morgan-Capner and D. W. Brown,
The burden of infection with HSV-1 and HSV-2 in England and Wales: Implications for the changing epidemiology of genital herpes., Sex Transm Infect, 76 (2000), 183-187.
doi: 10.1136/sti.76.3.183. |
[21] |
A. Wald and K. Link,
Risk of human immunodeficiency virus infection in herpes simplex virus type 2-seropositive persons: a meta-analysis, J Infect Dis, 185 (2002), 45-52.
doi: 10.1086/338231. |
[22] |
H. Weiss,
Epidemiology of herpes simplex virus type 2 infection in the developing world, Herpes, 11 (2004), 24A-35A.
|
show all references
References:
[1] |
L. J. Abu-Raddad, A. S. Magaret, C. Celum, A. Wald, I. M. Longini, S. G. Self and L. Corey, Genital herpes has played a more important role than any other sexually transmitted infection in driving hiv prevalence in africa,
PLoS ONE, 3 (2008), e2230. |
[2] |
B. Auvert, R. Ballard, C. Campbell, M. Caraël, M. Carton, G. Fehler, E. Gouws, C. MacPhail, D. Taljaard, J. V. Dam and B. Williams,
Hiv infection among youth in a south african mining town is associated with herpes simplex virus-2 seropositivity and sexual behaviour, AIDS, 15 (2001), 885-898.
|
[3] |
J. M. Baeten, D. Donnell, P. Ndase, N. R. Mugo, J. D. Campbell, J. Wangisi, J. W. Tappero, E. A. Bukusi, C. R. Cohen, E. Katabira, A. Ronald, E. Tumwesigye, E. Were, K. H. Fife, J. Kiarie, C. Farquhar, G. John-Stewart, A. Kakia, J. Odoyo, A. Mucunguzi, E. Nakku-Joloba, R. Twesigye, K. Ngure, C. Apaka, H. Tamooh, F. Gabona, A. Mujugira, D. Panteleeff, K. K. Thomas, L. Kidoguchi, M. Krows, J. Revall, S. Morrison, H. Haugen, M. Emmanuel-Ogier, L. Ondrejcek, R. W. Coombs, L. Frenkel, C. Hendrix, N. N. Bumpus, D. Bangsberg, J. E. Haberer, W. S. Stevens, J. R. Lingappa and C. Celum,
Antiretroviral prophylaxis for HIV prevention in heterosexual men and women, N Engl J Med, 367 (2012), 399-410.
|
[4] |
R. V. Barnabas, E. L. Webb, H. A. Weiss and J. N. Wasserheit,
The role of coinfections in HIV epidemic trajectory and positive prevention, AIDS, 25 (2011), 1559-1573.
|
[5] |
M.-C. Boily, R. F. Baggaley, L. Wang, B. Masse, R. G. White, R. J. Hayes and M. Alary, Heterosexual risk of hiv-1 infection per sexual act: Systematic review and meta-analysis of observational studies, Lancet Infect Dis, 9 (2009), 118–129, URL http://linkinghub.elsevier.com/retrieve/pii/S1473-3099(09)70021-0. |
[6] |
R. Burden and J. Faires,
Numerical Analysis, Cengage Learning, 2010. |
[7] |
Cohen, Chen, McCauley, Gamble, Hosseinipour, Kumarasamy, Hakim, Kumwenda, Grinsztejn, Pilotto, Godbole, Mehendale, Chariyalertsak, Santos, Mayer, Hoffman, Eshleman, Piwowar-Manning, Wang, Makhema, Mills, de Bruyn, Sanne, Eron, Gallant, Havlir, Swindells, Ribaudo, Elharrar, Burns, Taha, Nielsen-Saines, Celentano, Essex, Fleming and HPTN 052 Study Team,
Prevention of HIV-1 infection with early antiretroviral therapy., N Engl J Med, 365 (2011), 493-505.
|
[8] |
M. Das, P. L. Chu, G. -M. Santos, S. Scheer, E. Vittinghoff, W. McFarland and G. N. Colfax, Decreases in community viral load are accompanied by reductions in new HIV infections in san francisco,
PLoS ONE, 5 (2010), e11068. |
[9] |
E. E. Freeman, H. A. Weiss, J. R. Glynn, P. L. Cross, J. A. Whitworth and R. J. Hayes,
Herpes simplex virus 2 infection increases hiv acquisition in men and women: Systematic review and meta-analysis of longitudinal studies, AIDS, 20 (2006), 73-83.
|
[10] |
D. Gerberry, B. G. Wagner, J. G. García-Lerma, W. Heneine and S. Blower,
Using geospatial modelling to optimize the rollout of antiretroviral-based pre-exposure HIV interventions in Sub-Saharan Africa, Nature Communications, 5 (2014), 1-15.
|
[11] |
R. M. Granich, C. F. Gilks, C. Dye, K. M. De Cock and B. G. Williams,
Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: A mathematical model, Lancet, 373 (2009), 48-57.
|
[12] |
R. H. Gray, M. J. Wawer, R. Brookmeyer, N. K. Sewankambo, D. Serwadda, F. Wabwire-Mangen, T. Lutalo, X. Li, T. vanCott, T. C. Quinn and R. P. Team,
Probability of hiv-1 transmission per coital act in monogamous, heterosexual, hiv-1-discordant couples in rakai, uganda, Lancet, 357 (2001), 1149-1153.
|
[13] |
R. J. Hayes, K. F. Schulz and F. A. Plummer,
The cofactor effect of genital ulcers on the per-exposure risk of hiv transmission in sub-saharan africa, J Trop Med Hyg, 98 (1995), 1-8.
|
[14] |
K. A. Powers, C. Poole, A. E. Pettifor and M. S. Cohen,
Rethinking the heterosexual infectivity of hiv-1: A systematic review and meta-analysis, Lancet Infect Dis, 8 (2008), 553-563.
doi: 10.1016/S1473-3099(08)70156-7. |
[15] |
J. A. Røttingen, D. W. Cameron and G. P. Garnett,
A systematic review of the epidemiologic interactions between classic sexually transmitted diseases and hiv: How much really is known?, Sex Transm Dis, 28 (2001), 579-597.
|
[16] |
J. S. Smith and N. J. Robinson,
Age-specific prevalence of infection with herpes simplex virus types 2 and 1: A global review, J Infect Dis, 186 (2002), 3-28.
|
[17] |
R. J. Smith and S. M. Blower,
Could disease-modifying HIV vaccines cause population-level perversity?, Lancet Infect Dis, 4 (2004), 636-639.
doi: 10.1016/S1473-3099(04)01148-X. |
[18] |
The World Bank, World development indicators, http://data.worldbank.org/data--catalog/world--development--indicators [Accessed: 25 Oct 2011], URL http://data.worldbank.org/data-catalog/world-development-indicators. |
[19] |
M. C. Thigpen, P. M. Kebaabetswe, L. A. Paxton, D. K. Smith, C. E. Rose, T. M. Segolodi, F. L. Henderson, S. R. Pathak, F. A. Soud, K. L. Chillag, R. Mutanhaurwa, L. I. Chirwa, M. Kasonde, D. Abebe, E. Buliva, R. J. Gvetadze, S. Johnson, T. Sukalac, V. T. Thomas, C. Hart, J. A. Johnson, C. K. Malotte, C. W. Hendrix and J. T. Brooks,
Antiretroviral preexposure prophylaxis for heterosexual HIV transmission in botswana, N Engl J Med, 367 (2012), 423-434.
doi: 10.1056/NEJMoa1110711. |
[20] |
A. J. Vyse, N. J. Gay, M. J. Slomka, R. Gopal, T. Gibbs, P. Morgan-Capner and D. W. Brown,
The burden of infection with HSV-1 and HSV-2 in England and Wales: Implications for the changing epidemiology of genital herpes., Sex Transm Infect, 76 (2000), 183-187.
doi: 10.1136/sti.76.3.183. |
[21] |
A. Wald and K. Link,
Risk of human immunodeficiency virus infection in herpes simplex virus type 2-seropositive persons: a meta-analysis, J Infect Dis, 185 (2002), 45-52.
doi: 10.1086/338231. |
[22] |
H. Weiss,
Epidemiology of herpes simplex virus type 2 infection in the developing world, Herpes, 11 (2004), 24A-35A.
|





Symbol | Baseline | Range | References | |
Model Parameters | ||||
Average time in sexually active population (years) | 35 | 30-40 | ||
Recruitment rate into the sexually active population (/yr) | | | ||
Diseased-induced mortality due to HIV infection (/yr) | | |||
Cofactor for increased HIV susceptibility due to HSV-2 infection | 1.80 | 1.4-2.4 | [9,21,13,1] | |
Cofactor for increased HIV infectivity due to HSV-2 infection | 1.45 | 1.2-1.7 | [1,12,17,4] | |
Cofactor for increased HSV-2 infectivity due to HIV infection | 1.30 | 1.2-1.5 | [1] | |
Calibration Conditions | ||||
HIV prevalence at endemic equilibrium (%) | 17 | 0.3-17 | [18] | |
HSV-2 prevalence at endemic equilibrium (%) | 50 | 4-50 | [2,16,22,20] | |
Calibration Parameters | ||||
Transmission coefficient for HIV | determined by calibration procedure | |||
Transmission coefficient for HSV-2 | determined by calibration procedure |
Symbol | Baseline | Range | References | |
Model Parameters | ||||
Average time in sexually active population (years) | 35 | 30-40 | ||
Recruitment rate into the sexually active population (/yr) | | | ||
Diseased-induced mortality due to HIV infection (/yr) | | |||
Cofactor for increased HIV susceptibility due to HSV-2 infection | 1.80 | 1.4-2.4 | [9,21,13,1] | |
Cofactor for increased HIV infectivity due to HSV-2 infection | 1.45 | 1.2-1.7 | [1,12,17,4] | |
Cofactor for increased HSV-2 infectivity due to HIV infection | 1.30 | 1.2-1.5 | [1] | |
Calibration Conditions | ||||
HIV prevalence at endemic equilibrium (%) | 17 | 0.3-17 | [18] | |
HSV-2 prevalence at endemic equilibrium (%) | 50 | 4-50 | [2,16,22,20] | |
Calibration Parameters | ||||
Transmission coefficient for HIV | determined by calibration procedure | |||
Transmission coefficient for HSV-2 | determined by calibration procedure |
| | | precision | ||
South Africa (HIV prevalence 15%, HSV-2 prevalence 50%) | |||||
0 | 0.0367143341 | 0.0705450591 | 0.0000000447 | 0.5949903301 | |
1 | 0.0528598059 | 0.0770336930 | 0.1775025497 | 0.4988482844 | |
2 | 0.0522429752 | 0.0764216142 | 0.1700166525 | 0.5000125340 | |
3 | 0.0522423466 | 0.0764181115 | 0.1700000000 | 0.5000000000 | |
United Kingdom (HIV prevalence 0.3%, HSV-2 prevalence 4%) | |||||
0 | 0.0353517304 | 0.0297663650 | 0.0000221420 | 0.0401412229 | |
1 | 0.0359324850 | 0.0297727618 | 0.0033368789 | 0.0399611984 | |
2 | 0.0359185167 | 0.0297727520 | 0.0030000000 | 0.0400000000 | |
| | | precision | ||
South Africa (HIV prevalence 15%, HSV-2 prevalence 50%) | |||||
0 | 0.0367143341 | 0.0705450591 | 0.0000000447 | 0.5949903301 | |
1 | 0.0528598059 | 0.0770336930 | 0.1775025497 | 0.4988482844 | |
2 | 0.0522429752 | 0.0764216142 | 0.1700166525 | 0.5000125340 | |
3 | 0.0522423466 | 0.0764181115 | 0.1700000000 | 0.5000000000 | |
United Kingdom (HIV prevalence 0.3%, HSV-2 prevalence 4%) | |||||
0 | 0.0353517304 | 0.0297663650 | 0.0000221420 | 0.0401412229 | |
1 | 0.0359324850 | 0.0297727618 | 0.0033368789 | 0.0399611984 | |
2 | 0.0359185167 | 0.0297727520 | 0.0030000000 | 0.0400000000 | |
Sampled parameter values and calibration conditions | Calibration results | ||||||||||||
| |||||||||||||
1 | 0.026 | 0.028 | 0.037 | 1.98 | 1.65 | 1.24 | 0.088 | 0.276 | 0.043 | 0.045 | 0.088 | 0.276 | 4 |
2 | 0.033 | 0.027 | 0.015 | 2.39 | 1.23 | 1.22 | 0.146 | 0.164 | 0.039 | 0.035 | 0.146 | 0.164 | 4 |
3 | 0.028 | 0.027 | 0.022 | 1.55 | 1.25 | 1.23 | 0.007 | 0.340 | 0.037 | 0.042 | 0.007 | 0.340 | 3 |
4 | 0.025 | 0.032 | 0.042 | 2.39 | 1.52 | 1.50 | 0.025 | 0.275 | 0.043 | 0.046 | 0.025 | 0.275 | 3 |
5 | 0.025 | 0.028 | 0.016 | 2.24 | 1.33 | 1.36 | 0.145 | 0.291 | 0.034 | 0.042 | 0.145 | 0.291 | 4 |
6 | 0.032 | 0.027 | 0.021 | 2.01 | 1.51 | 1.28 | 0.123 | 0.294 | 0.034 | 0.042 | 0.123 | 0.294 | 4 |
7 | 0.031 | 0.033 | 0.033 | 1.89 | 1.57 | 1.41 | 0.065 | 0.290 | 0.043 | 0.049 | 0.065 | 0.290 | 4 |
8 | 0.031 | 0.030 | 0.020 | 1.67 | 1.67 | 1.48 | 0.110 | 0.330 | 0.034 | 0.046 | 0.110 | 0.330 | 4 |
9 | 0.027 | 0.028 | 0.030 | 2.19 | 1.29 | 1.45 | 0.016 | 0.409 | 0.033 | 0.048 | 0.016 | 0.409 | 3 |
10 | 0.029 | 0.028 | 0.029 | 1.84 | 1.67 | 1.47 | 0.170 | 0.134 | 0.054 | 0.038 | 0.170 | 0.134 | 4 |
11 | 0.025 | 0.030 | 0.035 | 1.66 | 1.40 | 1.47 | 0.147 | 0.477 | 0.046 | 0.066 | 0.147 | 0.477 | 4 |
12 | 0.032 | 0.028 | 0.022 | 1.56 | 1.24 | 1.37 | 0.143 | 0.176 | 0.050 | 0.037 | 0.143 | 0.176 | 4 |
13 | 0.026 | 0.028 | 0.040 | 1.59 | 1.54 | 1.38 | 0.026 | 0.419 | 0.041 | 0.050 | 0.026 | 0.419 | 3 |
14 | 0.027 | 0.028 | 0.048 | 2.14 | 1.41 | 1.33 | 0.025 | 0.152 | 0.059 | 0.036 | 0.025 | 0.152 | 3 |
15 | 0.031 | 0.027 | 0.044 | 1.69 | 1.47 | 1.43 | 0.121 | 0.312 | 0.055 | 0.048 | 0.121 | 0.312 | 4 |
16 | 0.029 | 0.033 | 0.045 | 1.43 | 1.42 | 1.44 | 0.162 | 0.354 | 0.067 | 0.061 | 0.162 | 0.354 | 4 |
17 | 0.028 | 0.029 | 0.033 | 1.54 | 1.31 | 1.48 | 0.118 | 0.234 | 0.056 | 0.042 | 0.118 | 0.234 | 4 |
18 | 0.028 | 0.029 | 0.012 | 1.59 | 1.58 | 1.32 | 0.027 | 0.377 | 0.026 | 0.047 | 0.027 | 0.377 | 3 |
19 | 0.026 | 0.029 | 0.029 | 1.87 | 1.24 | 1.37 | 0.074 | 0.315 | 0.044 | 0.045 | 0.074 | 0.315 | 4 |
20 | 0.033 | 0.031 | 0.021 | 2.39 | 1.41 | 1.49 | 0.145 | 0.127 | 0.047 | 0.037 | 0.145 | 0.127 | 4 |
21 | 0.030 | 0.031 | 0.017 | 1.60 | 1.38 | 1.39 | 0.024 | 0.054 | 0.046 | 0.033 | 0.024 | 0.054 | 3 |
22 | 0.025 | 0.032 | 0.010 | 1.46 | 1.46 | 1.30 | 0.098 | 0.412 | 0.031 | 0.055 | 0.098 | 0.412 | 4 |
23 | 0.029 | 0.028 | 0.046 | 1.64 | 1.59 | 1.30 | 0.150 | 0.256 | 0.060 | 0.049 | 0.150 | 0.256 | 4 |
24 | 0.031 | 0.026 | 0.044 | 2.16 | 1.57 | 1.50 | 0.040 | 0.360 | 0.038 | 0.044 | 0.040 | 0.360 | 4 |
25 | 0.028 | 0.030 | 0.022 | 2.05 | 1.54 | 1.24 | 0.132 | 0.093 | 0.051 | 0.038 | 0.132 | 0.093 | 4 |
26 | 0.033 | 0.027 | 0.019 | 1.64 | 1.54 | 1.35 | 0.140 | 0.384 | 0.033 | 0.048 | 0.140 | 0.384 | 4 |
27 | 0.033 | 0.028 | 0.025 | 2.12 | 1.23 | 1.43 | 0.125 | 0.488 | 0.034 | 0.058 | 0.125 | 0.488 | 4 |
28 | 0.026 | 0.030 | 0.024 | 2.06 | 1.20 | 1.46 | 0.050 | 0.497 | 0.033 | 0.062 | 0.050 | 0.497 | 3 |
29 | 0.028 | 0.032 | 0.021 | 2.35 | 1.65 | 1.26 | 0.117 | 0.419 | 0.027 | 0.059 | 0.117 | 0.419 | 4 |
30 | 0.032 | 0.027 | 0.014 | 2.15 | 1.45 | 1.40 | 0.007 | 0.336 | 0.023 | 0.041 | 0.007 | 0.336 | 3 |
31 | 0.029 | 0.028 | 0.021 | 2.30 | 1.32 | 1.24 | 0.007 | 0.416 | 0.026 | 0.048 | 0.007 | 0.416 | 3 |
32 | 0.031 | 0.032 | 0.028 | 1.98 | 1.46 | 1.34 | 0.143 | 0.166 | 0.054 | 0.044 | 0.143 | 0.166 | 4 |
33 | 0.025 | 0.030 | 0.012 | 2.31 | 1.67 | 1.36 | 0.160 | 0.044 | 0.045 | 0.032 | 0.160 | 0.044 | 4 |
34 | 0.027 | 0.025 | 0.018 | 1.66 | 1.25 | 1.24 | 0.122 | 0.099 | 0.045 | 0.031 | 0.122 | 0.099 | 3 |
35 | 0.029 | 0.032 | 0.024 | 2.00 | 1.36 | 1.38 | 0.141 | 0.197 | 0.049 | 0.044 | 0.141 | 0.197 | 4 |
36 | 0.029 | 0.031 | 0.012 | 2.01 | 1.20 | 1.45 | 0.006 | 0.367 | 0.027 | 0.049 | 0.006 | 0.367 | 3 |
37 | 0.026 | 0.028 | 0.047 | 2.07 | 1.60 | 1.37 | 0.155 | 0.070 | 0.076 | 0.041 | 0.155 | 0.070 | 4 |
38 | 0.032 | 0.027 | 0.027 | 1.84 | 1.60 | 1.42 | 0.161 | 0.397 | 0.036 | 0.051 | 0.161 | 0.397 | 4 |
39 | 0.033 | 0.032 | 0.043 | 1.88 | 1.32 | 1.38 | 0.021 | 0.412 | 0.047 | 0.055 | 0.021 | 0.412 | 3 |
40 | 0.026 | 0.033 | 0.037 | 1.83 | 1.66 | 1.34 | 0.022 | 0.390 | 0.038 | 0.055 | 0.022 | 0.390 | 3 |
41 | 0.033 | 0.032 | 0.035 | 1.86 | 1.24 | 1.26 | 0.073 | 0.049 | 0.068 | 0.038 | 0.073 | 0.049 | 3 |
42 | 0.027 | 0.026 | 0.031 | 2.14 | 1.37 | 1.33 | 0.113 | 0.069 | 0.057 | 0.033 | 0.113 | 0.069 | 3 |
43 | 0.033 | 0.027 | 0.022 | 1.95 | 1.41 | 1.28 | 0.126 | 0.217 | 0.041 | 0.039 | 0.126 | 0.217 | 4 |
44 | 0.030 | 0.026 | 0.014 | 2.34 | 1.39 | 1.22 | 0.119 | 0.317 | 0.027 | 0.041 | 0.119 | 0.317 | 4 |
45 | 0.029 | 0.028 | 0.021 | 2.06 | 1.38 | 1.22 | 0.048 | 0.480 | 0.026 | 0.055 | 0.048 | 0.480 | 4 |
46 | 0.026 | 0.027 | 0.031 | 1.77 | 1.67 | 1.25 | 0.143 | 0.439 | 0.036 | 0.057 | 0.143 | 0.439 | 4 |
47 | 0.029 | 0.032 | 0.031 | 2.09 | 1.23 | 1.40 | 0.030 | 0.337 | 0.042 | 0.050 | 0.030 | 0.337 | 3 |
48 | 0.028 | 0.029 | 0.025 | 1.67 | 1.22 | 1.35 | 0.160 | 0.303 | 0.049 | 0.047 | 0.160 | 0.303 | 4 |
49 | 0.033 | 0.033 | 0.040 | 1.83 | 1.62 | 1.47 | 0.041 | 0.375 | 0.042 | 0.055 | 0.041 | 0.375 | 4 |
50 | 0.029 | 0.030 | 0.045 | 2.23 | 1.22 | 1.39 | 0.044 | 0.101 | 0.067 | 0.037 | 0.044 | 0.101 | 3 |
Sampled parameter values and calibration conditions | Calibration results | ||||||||||||
| |||||||||||||
1 | 0.026 | 0.028 | 0.037 | 1.98 | 1.65 | 1.24 | 0.088 | 0.276 | 0.043 | 0.045 | 0.088 | 0.276 | 4 |
2 | 0.033 | 0.027 | 0.015 | 2.39 | 1.23 | 1.22 | 0.146 | 0.164 | 0.039 | 0.035 | 0.146 | 0.164 | 4 |
3 | 0.028 | 0.027 | 0.022 | 1.55 | 1.25 | 1.23 | 0.007 | 0.340 | 0.037 | 0.042 | 0.007 | 0.340 | 3 |
4 | 0.025 | 0.032 | 0.042 | 2.39 | 1.52 | 1.50 | 0.025 | 0.275 | 0.043 | 0.046 | 0.025 | 0.275 | 3 |
5 | 0.025 | 0.028 | 0.016 | 2.24 | 1.33 | 1.36 | 0.145 | 0.291 | 0.034 | 0.042 | 0.145 | 0.291 | 4 |
6 | 0.032 | 0.027 | 0.021 | 2.01 | 1.51 | 1.28 | 0.123 | 0.294 | 0.034 | 0.042 | 0.123 | 0.294 | 4 |
7 | 0.031 | 0.033 | 0.033 | 1.89 | 1.57 | 1.41 | 0.065 | 0.290 | 0.043 | 0.049 | 0.065 | 0.290 | 4 |
8 | 0.031 | 0.030 | 0.020 | 1.67 | 1.67 | 1.48 | 0.110 | 0.330 | 0.034 | 0.046 | 0.110 | 0.330 | 4 |
9 | 0.027 | 0.028 | 0.030 | 2.19 | 1.29 | 1.45 | 0.016 | 0.409 | 0.033 | 0.048 | 0.016 | 0.409 | 3 |
10 | 0.029 | 0.028 | 0.029 | 1.84 | 1.67 | 1.47 | 0.170 | 0.134 | 0.054 | 0.038 | 0.170 | 0.134 | 4 |
11 | 0.025 | 0.030 | 0.035 | 1.66 | 1.40 | 1.47 | 0.147 | 0.477 | 0.046 | 0.066 | 0.147 | 0.477 | 4 |
12 | 0.032 | 0.028 | 0.022 | 1.56 | 1.24 | 1.37 | 0.143 | 0.176 | 0.050 | 0.037 | 0.143 | 0.176 | 4 |
13 | 0.026 | 0.028 | 0.040 | 1.59 | 1.54 | 1.38 | 0.026 | 0.419 | 0.041 | 0.050 | 0.026 | 0.419 | 3 |
14 | 0.027 | 0.028 | 0.048 | 2.14 | 1.41 | 1.33 | 0.025 | 0.152 | 0.059 | 0.036 | 0.025 | 0.152 | 3 |
15 | 0.031 | 0.027 | 0.044 | 1.69 | 1.47 | 1.43 | 0.121 | 0.312 | 0.055 | 0.048 | 0.121 | 0.312 | 4 |
16 | 0.029 | 0.033 | 0.045 | 1.43 | 1.42 | 1.44 | 0.162 | 0.354 | 0.067 | 0.061 | 0.162 | 0.354 | 4 |
17 | 0.028 | 0.029 | 0.033 | 1.54 | 1.31 | 1.48 | 0.118 | 0.234 | 0.056 | 0.042 | 0.118 | 0.234 | 4 |
18 | 0.028 | 0.029 | 0.012 | 1.59 | 1.58 | 1.32 | 0.027 | 0.377 | 0.026 | 0.047 | 0.027 | 0.377 | 3 |
19 | 0.026 | 0.029 | 0.029 | 1.87 | 1.24 | 1.37 | 0.074 | 0.315 | 0.044 | 0.045 | 0.074 | 0.315 | 4 |
20 | 0.033 | 0.031 | 0.021 | 2.39 | 1.41 | 1.49 | 0.145 | 0.127 | 0.047 | 0.037 | 0.145 | 0.127 | 4 |
21 | 0.030 | 0.031 | 0.017 | 1.60 | 1.38 | 1.39 | 0.024 | 0.054 | 0.046 | 0.033 | 0.024 | 0.054 | 3 |
22 | 0.025 | 0.032 | 0.010 | 1.46 | 1.46 | 1.30 | 0.098 | 0.412 | 0.031 | 0.055 | 0.098 | 0.412 | 4 |
23 | 0.029 | 0.028 | 0.046 | 1.64 | 1.59 | 1.30 | 0.150 | 0.256 | 0.060 | 0.049 | 0.150 | 0.256 | 4 |
24 | 0.031 | 0.026 | 0.044 | 2.16 | 1.57 | 1.50 | 0.040 | 0.360 | 0.038 | 0.044 | 0.040 | 0.360 | 4 |
25 | 0.028 | 0.030 | 0.022 | 2.05 | 1.54 | 1.24 | 0.132 | 0.093 | 0.051 | 0.038 | 0.132 | 0.093 | 4 |
26 | 0.033 | 0.027 | 0.019 | 1.64 | 1.54 | 1.35 | 0.140 | 0.384 | 0.033 | 0.048 | 0.140 | 0.384 | 4 |
27 | 0.033 | 0.028 | 0.025 | 2.12 | 1.23 | 1.43 | 0.125 | 0.488 | 0.034 | 0.058 | 0.125 | 0.488 | 4 |
28 | 0.026 | 0.030 | 0.024 | 2.06 | 1.20 | 1.46 | 0.050 | 0.497 | 0.033 | 0.062 | 0.050 | 0.497 | 3 |
29 | 0.028 | 0.032 | 0.021 | 2.35 | 1.65 | 1.26 | 0.117 | 0.419 | 0.027 | 0.059 | 0.117 | 0.419 | 4 |
30 | 0.032 | 0.027 | 0.014 | 2.15 | 1.45 | 1.40 | 0.007 | 0.336 | 0.023 | 0.041 | 0.007 | 0.336 | 3 |
31 | 0.029 | 0.028 | 0.021 | 2.30 | 1.32 | 1.24 | 0.007 | 0.416 | 0.026 | 0.048 | 0.007 | 0.416 | 3 |
32 | 0.031 | 0.032 | 0.028 | 1.98 | 1.46 | 1.34 | 0.143 | 0.166 | 0.054 | 0.044 | 0.143 | 0.166 | 4 |
33 | 0.025 | 0.030 | 0.012 | 2.31 | 1.67 | 1.36 | 0.160 | 0.044 | 0.045 | 0.032 | 0.160 | 0.044 | 4 |
34 | 0.027 | 0.025 | 0.018 | 1.66 | 1.25 | 1.24 | 0.122 | 0.099 | 0.045 | 0.031 | 0.122 | 0.099 | 3 |
35 | 0.029 | 0.032 | 0.024 | 2.00 | 1.36 | 1.38 | 0.141 | 0.197 | 0.049 | 0.044 | 0.141 | 0.197 | 4 |
36 | 0.029 | 0.031 | 0.012 | 2.01 | 1.20 | 1.45 | 0.006 | 0.367 | 0.027 | 0.049 | 0.006 | 0.367 | 3 |
37 | 0.026 | 0.028 | 0.047 | 2.07 | 1.60 | 1.37 | 0.155 | 0.070 | 0.076 | 0.041 | 0.155 | 0.070 | 4 |
38 | 0.032 | 0.027 | 0.027 | 1.84 | 1.60 | 1.42 | 0.161 | 0.397 | 0.036 | 0.051 | 0.161 | 0.397 | 4 |
39 | 0.033 | 0.032 | 0.043 | 1.88 | 1.32 | 1.38 | 0.021 | 0.412 | 0.047 | 0.055 | 0.021 | 0.412 | 3 |
40 | 0.026 | 0.033 | 0.037 | 1.83 | 1.66 | 1.34 | 0.022 | 0.390 | 0.038 | 0.055 | 0.022 | 0.390 | 3 |
41 | 0.033 | 0.032 | 0.035 | 1.86 | 1.24 | 1.26 | 0.073 | 0.049 | 0.068 | 0.038 | 0.073 | 0.049 | 3 |
42 | 0.027 | 0.026 | 0.031 | 2.14 | 1.37 | 1.33 | 0.113 | 0.069 | 0.057 | 0.033 | 0.113 | 0.069 | 3 |
43 | 0.033 | 0.027 | 0.022 | 1.95 | 1.41 | 1.28 | 0.126 | 0.217 | 0.041 | 0.039 | 0.126 | 0.217 | 4 |
44 | 0.030 | 0.026 | 0.014 | 2.34 | 1.39 | 1.22 | 0.119 | 0.317 | 0.027 | 0.041 | 0.119 | 0.317 | 4 |
45 | 0.029 | 0.028 | 0.021 | 2.06 | 1.38 | 1.22 | 0.048 | 0.480 | 0.026 | 0.055 | 0.048 | 0.480 | 4 |
46 | 0.026 | 0.027 | 0.031 | 1.77 | 1.67 | 1.25 | 0.143 | 0.439 | 0.036 | 0.057 | 0.143 | 0.439 | 4 |
47 | 0.029 | 0.032 | 0.031 | 2.09 | 1.23 | 1.40 | 0.030 | 0.337 | 0.042 | 0.050 | 0.030 | 0.337 | 3 |
48 | 0.028 | 0.029 | 0.025 | 1.67 | 1.22 | 1.35 | 0.160 | 0.303 | 0.049 | 0.047 | 0.160 | 0.303 | 4 |
49 | 0.033 | 0.033 | 0.040 | 1.83 | 1.62 | 1.47 | 0.041 | 0.375 | 0.042 | 0.055 | 0.041 | 0.375 | 4 |
50 | 0.029 | 0.030 | 0.045 | 2.23 | 1.22 | 1.39 | 0.044 | 0.101 | 0.067 | 0.037 | 0.044 | 0.101 | 3 |
Symbol | Baseline | Range | References | |
Model Parameters | ||||
Background mortality rate (/yr) | 0.018 | | [11] | |
Recruitment rate into the population (/yr) | 0.018 | | | |
Location of transmission term | 0.055 | 0.05-50 | [11] | |
Shape of transmission term | 0.996 | 0.90-30 | [11] | |
Rate of HIV progression (/yr) | 0.303 | 0.1-0.4 | [11] | |
Calibration Conditions | ||||
HIV prevalence at endemic equilibrium | 0.17 | 0.3-17 | [18] | |
Calibration Parameters | ||||
Initial value of transmission term (/yr) | determined by calibration procedure |
Symbol | Baseline | Range | References | |
Model Parameters | ||||
Background mortality rate (/yr) | 0.018 | | [11] | |
Recruitment rate into the population (/yr) | 0.018 | | | |
Location of transmission term | 0.055 | 0.05-50 | [11] | |
Shape of transmission term | 0.996 | 0.90-30 | [11] | |
Rate of HIV progression (/yr) | 0.303 | 0.1-0.4 | [11] | |
Calibration Conditions | ||||
HIV prevalence at endemic equilibrium | 0.17 | 0.3-17 | [18] | |
Calibration Parameters | ||||
Initial value of transmission term (/yr) | determined by calibration procedure |
Sampled parameters and calibration condition | Calibration results | |||||||
| ||||||||
1 | 0.018 | 0.021 | 34.3 | 29.1 | 0.115 | 0.104 | 0.115 | 2 |
2 | 0.028 | 0.024 | 31.7 | 14.6 | 0.019 | 0.065 | 0.019 | 2 |
3 | 0.022 | 0.025 | 5.8 | 4.9 | 0.126 | 0.066 | 0.126 | 2 |
4 | 0.021 | 0.019 | 30.2 | 6.1 | 0.142 | 0.044 | 0.142 | 2 |
5 | 0.028 | 0.017 | 35.9 | 5.7 | 0.006 | 0.097 | 0.006 | 2 |
6 | 0.026 | 0.028 | 8.7 | 22.0 | 0.015 | 0.049 | 0.015 | 2 |
7 | 0.031 | 0.018 | 6.0 | 27.3 | 0.061 | 0.087 | 0.061 | 2 |
8 | 0.030 | 0.019 | 29.9 | 17.2 | 0.014 | 0.077 | 0.014 | 2 |
9 | 0.024 | 0.026 | 32.4 | 6.3 | 0.073 | 0.078 | 0.073 | 2 |
10 | 0.022 | 0.022 | 47.6 | 18.5 | 0.125 | 0.098 | 0.125 | 2 |
11 | 0.022 | 0.030 | 25.0 | 19.3 | 0.160 | 0.124 | 0.160 | 2 |
12 | 0.023 | 0.030 | 49.1 | 10.6 | 0.114 | 0.059 | 0.114 | 2 |
13 | 0.032 | 0.017 | 17.4 | 14.4 | 0.061 | 0.041 | 0.061 | 2 |
14 | 0.025 | 0.030 | 9.0 | 3.0 | 0.140 | 0.063 | 0.140 | 2 |
15 | 0.020 | 0.022 | 8.3 | 14.9 | 0.093 | 0.126 | 0.093 | 2 |
16 | 0.024 | 0.028 | 24.0 | 23.0 | 0.060 | 0.077 | 0.060 | 2 |
17 | 0.029 | 0.032 | 8.0 | 24.5 | 0.023 | 0.108 | 0.023 | 2 |
18 | 0.025 | 0.025 | 25.3 | 15.1 | 0.119 | 0.109 | 0.119 | 2 |
19 | 0.018 | 0.031 | 18.8 | 29.1 | 0.126 | 0.084 | 0.126 | 2 |
20 | 0.031 | 0.026 | 41.9 | 24.7 | 0.075 | 0.107 | 0.075 | 2 |
21 | 0.027 | 0.018 | 22.6 | 18.3 | 0.131 | 0.102 | 0.131 | 2 |
22 | 0.027 | 0.019 | 23.9 | 12.6 | 0.106 | 0.094 | 0.106 | 2 |
23 | 0.031 | 0.026 | 28.6 | 10.0 | 0.086 | 0.095 | 0.086 | 2 |
24 | 0.019 | 0.027 | 45.3 | 6.9 | 0.067 | 0.075 | 0.067 | 2 |
25 | 0.025 | 0.033 | 42.0 | 7.9 | 0.040 | 0.102 | 0.040 | 2 |
26 | 0.020 | 0.027 | 36.7 | 21.5 | 0.112 | 0.085 | 0.112 | 2 |
27 | 0.020 | 0.020 | 24.4 | 7.2 | 0.088 | 0.049 | 0.088 | 2 |
28 | 0.021 | 0.026 | 49.6 | 25.3 | 0.154 | 0.123 | 0.154 | 2 |
29 | 0.030 | 0.026 | 9.8 | 12.5 | 0.100 | 0.072 | 0.100 | 2 |
30 | 0.021 | 0.019 | 2.4 | 22.5 | 0.058 | 0.106 | 0.058 | 2 |
31 | 0.022 | 0.026 | 4.6 | 23.2 | 0.098 | 0.101 | 0.098 | 2 |
32 | 0.026 | 0.022 | 46.7 | 17.7 | 0.108 | 0.090 | 0.108 | 2 |
33 | 0.029 | 0.024 | 5.8 | 9.6 | 0.120 | 0.125 | 0.120 | 2 |
34 | 0.023 | 0.030 | 9.5 | 17.1 | 0.027 | 0.087 | 0.027 | 2 |
35 | 0.025 | 0.024 | 0.7 | 23.5 | 0.111 | 0.117 | 0.111 | 2 |
36 | 0.021 | 0.030 | 16.0 | 21.0 | 0.023 | 0.101 | 0.023 | 2 |
37 | 0.027 | 0.018 | 29.4 | 6.3 | 0.165 | 0.123 | 0.165 | 2 |
38 | 0.025 | 0.033 | 48.2 | 6.1 | 0.071 | 0.096 | 0.071 | 2 |
39 | 0.027 | 0.030 | 12.0 | 22.4 | 0.057 | 0.071 | 0.057 | 2 |
40 | 0.025 | 0.033 | 43.6 | 4.3 | 0.017 | 0.059 | 0.017 | 2 |
41 | 0.031 | 0.031 | 1.7 | 13.0 | 0.151 | 0.075 | 0.151 | 2 |
42 | 0.031 | 0.031 | 26.1 | 11.1 | 0.041 | 0.077 | 0.041 | 2 |
43 | 0.022 | 0.024 | 39.9 | 16.9 | 0.100 | 0.100 | 0.100 | 2 |
44 | 0.029 | 0.022 | 17.7 | 13.2 | 0.103 | 0.061 | 0.103 | 2 |
45 | 0.023 | 0.024 | 6.7 | 21.4 | 0.158 | 0.117 | 0.158 | 2 |
46 | 0.028 | 0.023 | 4.2 | 10.5 | 0.082 | 0.051 | 0.082 | 2 |
47 | 0.023 | 0.031 | 13.1 | 18.4 | 0.022 | 0.084 | 0.022 | 2 |
48 | 0.031 | 0.022 | 46.3 | 28.3 | 0.058 | 0.118 | 0.058 | 2 |
49 | 0.020 | 0.025 | 42.7 | 27.7 | 0.077 | 0.112 | 0.077 | 2 |
50 | 0.024 | 0.030 | 46.1 | 2.2 | 0.082 | 0.085 | 0.082 | 2 |
Sampled parameters and calibration condition | Calibration results | |||||||
| ||||||||
1 | 0.018 | 0.021 | 34.3 | 29.1 | 0.115 | 0.104 | 0.115 | 2 |
2 | 0.028 | 0.024 | 31.7 | 14.6 | 0.019 | 0.065 | 0.019 | 2 |
3 | 0.022 | 0.025 | 5.8 | 4.9 | 0.126 | 0.066 | 0.126 | 2 |
4 | 0.021 | 0.019 | 30.2 | 6.1 | 0.142 | 0.044 | 0.142 | 2 |
5 | 0.028 | 0.017 | 35.9 | 5.7 | 0.006 | 0.097 | 0.006 | 2 |
6 | 0.026 | 0.028 | 8.7 | 22.0 | 0.015 | 0.049 | 0.015 | 2 |
7 | 0.031 | 0.018 | 6.0 | 27.3 | 0.061 | 0.087 | 0.061 | 2 |
8 | 0.030 | 0.019 | 29.9 | 17.2 | 0.014 | 0.077 | 0.014 | 2 |
9 | 0.024 | 0.026 | 32.4 | 6.3 | 0.073 | 0.078 | 0.073 | 2 |
10 | 0.022 | 0.022 | 47.6 | 18.5 | 0.125 | 0.098 | 0.125 | 2 |
11 | 0.022 | 0.030 | 25.0 | 19.3 | 0.160 | 0.124 | 0.160 | 2 |
12 | 0.023 | 0.030 | 49.1 | 10.6 | 0.114 | 0.059 | 0.114 | 2 |
13 | 0.032 | 0.017 | 17.4 | 14.4 | 0.061 | 0.041 | 0.061 | 2 |
14 | 0.025 | 0.030 | 9.0 | 3.0 | 0.140 | 0.063 | 0.140 | 2 |
15 | 0.020 | 0.022 | 8.3 | 14.9 | 0.093 | 0.126 | 0.093 | 2 |
16 | 0.024 | 0.028 | 24.0 | 23.0 | 0.060 | 0.077 | 0.060 | 2 |
17 | 0.029 | 0.032 | 8.0 | 24.5 | 0.023 | 0.108 | 0.023 | 2 |
18 | 0.025 | 0.025 | 25.3 | 15.1 | 0.119 | 0.109 | 0.119 | 2 |
19 | 0.018 | 0.031 | 18.8 | 29.1 | 0.126 | 0.084 | 0.126 | 2 |
20 | 0.031 | 0.026 | 41.9 | 24.7 | 0.075 | 0.107 | 0.075 | 2 |
21 | 0.027 | 0.018 | 22.6 | 18.3 | 0.131 | 0.102 | 0.131 | 2 |
22 | 0.027 | 0.019 | 23.9 | 12.6 | 0.106 | 0.094 | 0.106 | 2 |
23 | 0.031 | 0.026 | 28.6 | 10.0 | 0.086 | 0.095 | 0.086 | 2 |
24 | 0.019 | 0.027 | 45.3 | 6.9 | 0.067 | 0.075 | 0.067 | 2 |
25 | 0.025 | 0.033 | 42.0 | 7.9 | 0.040 | 0.102 | 0.040 | 2 |
26 | 0.020 | 0.027 | 36.7 | 21.5 | 0.112 | 0.085 | 0.112 | 2 |
27 | 0.020 | 0.020 | 24.4 | 7.2 | 0.088 | 0.049 | 0.088 | 2 |
28 | 0.021 | 0.026 | 49.6 | 25.3 | 0.154 | 0.123 | 0.154 | 2 |
29 | 0.030 | 0.026 | 9.8 | 12.5 | 0.100 | 0.072 | 0.100 | 2 |
30 | 0.021 | 0.019 | 2.4 | 22.5 | 0.058 | 0.106 | 0.058 | 2 |
31 | 0.022 | 0.026 | 4.6 | 23.2 | 0.098 | 0.101 | 0.098 | 2 |
32 | 0.026 | 0.022 | 46.7 | 17.7 | 0.108 | 0.090 | 0.108 | 2 |
33 | 0.029 | 0.024 | 5.8 | 9.6 | 0.120 | 0.125 | 0.120 | 2 |
34 | 0.023 | 0.030 | 9.5 | 17.1 | 0.027 | 0.087 | 0.027 | 2 |
35 | 0.025 | 0.024 | 0.7 | 23.5 | 0.111 | 0.117 | 0.111 | 2 |
36 | 0.021 | 0.030 | 16.0 | 21.0 | 0.023 | 0.101 | 0.023 | 2 |
37 | 0.027 | 0.018 | 29.4 | 6.3 | 0.165 | 0.123 | 0.165 | 2 |
38 | 0.025 | 0.033 | 48.2 | 6.1 | 0.071 | 0.096 | 0.071 | 2 |
39 | 0.027 | 0.030 | 12.0 | 22.4 | 0.057 | 0.071 | 0.057 | 2 |
40 | 0.025 | 0.033 | 43.6 | 4.3 | 0.017 | 0.059 | 0.017 | 2 |
41 | 0.031 | 0.031 | 1.7 | 13.0 | 0.151 | 0.075 | 0.151 | 2 |
42 | 0.031 | 0.031 | 26.1 | 11.1 | 0.041 | 0.077 | 0.041 | 2 |
43 | 0.022 | 0.024 | 39.9 | 16.9 | 0.100 | 0.100 | 0.100 | 2 |
44 | 0.029 | 0.022 | 17.7 | 13.2 | 0.103 | 0.061 | 0.103 | 2 |
45 | 0.023 | 0.024 | 6.7 | 21.4 | 0.158 | 0.117 | 0.158 | 2 |
46 | 0.028 | 0.023 | 4.2 | 10.5 | 0.082 | 0.051 | 0.082 | 2 |
47 | 0.023 | 0.031 | 13.1 | 18.4 | 0.022 | 0.084 | 0.022 | 2 |
48 | 0.031 | 0.022 | 46.3 | 28.3 | 0.058 | 0.118 | 0.058 | 2 |
49 | 0.020 | 0.025 | 42.7 | 27.7 | 0.077 | 0.112 | 0.077 | 2 |
50 | 0.024 | 0.030 | 46.1 | 2.2 | 0.082 | 0.085 | 0.082 | 2 |
Symbol | Range | References | |
Model Parameters | |||
Background mortality rate (/yr) | | [11] | |
Recruitment rate into the population (/yr) | | | |
Location of HIV transmission term | 0.05-50 | [11] | |
Shape of HIV transmission term | 0.90-30 | [11] | |
Rate of HIV progression (/yr) | 0.1-0.4 | [11] | |
Calibration Conditions | |||
HIV prevalence at endemic equilibrium (/yr) | 0.3-17 | [18] | |
HSV-2 prevalence at endemic equilibrium (/yr) | 4-50 | [2,16,22,20] | |
Calibration Parameters | |||
Initial value of HIV transmission term (/yr) | determined by calibration procedure | ||
Initial value of HSV-2 transmission term (/yr) | determined by calibration procedure |
Symbol | Range | References | |
Model Parameters | |||
Background mortality rate (/yr) | | [11] | |
Recruitment rate into the population (/yr) | | | |
Location of HIV transmission term | 0.05-50 | [11] | |
Shape of HIV transmission term | 0.90-30 | [11] | |
Rate of HIV progression (/yr) | 0.1-0.4 | [11] | |
Calibration Conditions | |||
HIV prevalence at endemic equilibrium (/yr) | 0.3-17 | [18] | |
HSV-2 prevalence at endemic equilibrium (/yr) | 4-50 | [2,16,22,20] | |
Calibration Parameters | |||
Initial value of HIV transmission term (/yr) | determined by calibration procedure | ||
Initial value of HSV-2 transmission term (/yr) | determined by calibration procedure |
Sampled parameters and calibration condition | Calibration results | |||||||||||
| ||||||||||||
1 | 0.033 | 0.030 | 0.136 | 25.388 | 7.775 | 0.100 | 0.429 | 0.040 | 0.057 | 0.100 | 0.429 | 4 |
2 | 0.026 | 0.025 | 0.294 | 25.452 | 10.004 | 0.061 | 0.433 | 0.057 | 0.053 | 0.061 | 0.433 | 4 |
3 | 0.022 | 0.032 | 0.268 | 9.053 | 18.416 | 0.065 | 0.333 | 0.066 | 0.055 | 0.065 | 0.333 | 4 |
4 | 0.027 | 0.022 | 0.159 | 30.943 | 15.777 | 0.107 | 0.286 | 0.042 | 0.038 | 0.107 | 0.286 | 4 |
5 | 0.020 | 0.032 | 0.184 | 35.273 | 19.612 | 0.025 | 0.484 | 0.033 | 0.063 | 0.025 | 0.484 | 4 |
6 | 0.019 | 0.017 | 0.363 | 46.871 | 29.933 | 0.081 | 0.050 | 0.105 | 0.029 | 0.081 | 0.050 | 4 |
7 | 0.021 | 0.026 | 0.164 | 35.976 | 10.444 | 0.050 | 0.437 | 0.034 | 0.050 | 0.050 | 0.437 | 4 |
8 | 0.017 | 0.023 | 0.149 | 45.299 | 27.869 | 0.013 | 0.349 | 0.031 | 0.035 | 0.013 | 0.349 | 4 |
9 | 0.018 | 0.022 | 0.122 | 2.960 | 2.103 | 0.161 | 0.067 | 0.050 | 0.031 | 0.161 | 0.067 | 4 |
10 | 0.020 | 0.025 | 0.210 | 47.955 | 15.737 | 0.099 | 0.044 | 0.072 | 0.034 | 0.099 | 0.044 | 4 |
11 | 0.018 | 0.021 | 0.120 | 22.432 | 23.321 | 0.114 | 0.424 | 0.028 | 0.042 | 0.114 | 0.424 | 4 |
12 | 0.032 | 0.023 | 0.155 | 27.625 | 4.781 | 0.107 | 0.234 | 0.044 | 0.037 | 0.107 | 0.234 | 4 |
13 | 0.029 | 0.027 | 0.324 | 36.150 | 6.654 | 0.087 | 0.303 | 0.063 | 0.051 | 0.087 | 0.303 | 4 |
14 | 0.018 | 0.020 | 0.144 | 29.338 | 26.770 | 0.008 | 0.357 | 0.027 | 0.032 | 0.008 | 0.357 | 4 |
15 | 0.019 | 0.032 | 0.377 | 42.820 | 16.166 | 0.168 | 0.403 | 0.084 | 0.086 | 0.168 | 0.403 | 4 |
16 | 0.028 | 0.017 | 0.126 | 15.874 | 24.707 | 0.160 | 0.237 | 0.041 | 0.030 | 0.160 | 0.237 | 4 |
17 | 0.021 | 0.024 | 0.275 | 14.494 | 1.718 | 0.097 | 0.111 | 0.111 | 0.047 | 0.097 | 0.111 | 4 |
18 | 0.032 | 0.026 | 0.254 | 14.086 | 11.617 | 0.085 | 0.231 | 0.053 | 0.044 | 0.085 | 0.231 | 4 |
19 | 0.020 | 0.030 | 0.300 | 18.883 | 1.811 | 0.022 | 0.358 | 0.054 | 0.051 | 0.022 | 0.358 | 4 |
20 | 0.024 | 0.024 | 0.274 | 5.479 | 9.004 | 0.161 | 0.068 | 0.091 | 0.043 | 0.161 | 0.068 | 4 |
21 | 0.033 | 0.024 | 0.149 | 26.541 | 10.778 | 0.003 | 0.325 | 0.032 | 0.035 | 0.003 | 0.325 | 4 |
22 | 0.024 | 0.031 | 0.173 | 0.848 | 2.736 | 0.019 | 0.206 | 0.050 | 0.040 | 0.019 | 0.206 | 4 |
23 | 0.017 | 0.020 | 0.147 | 35.029 | 14.683 | 0.102 | 0.117 | 0.046 | 0.028 | 0.102 | 0.117 | 4 |
24 | 0.026 | 0.030 | 0.121 | 23.521 | 10.510 | 0.114 | 0.340 | 0.036 | 0.049 | 0.114 | 0.340 | 4 |
25 | 0.029 | 0.030 | 0.169 | 35.260 | 8.151 | 0.122 | 0.496 | 0.035 | 0.070 | 0.122 | 0.496 | 4 |
26 | 0.028 | 0.031 | 0.357 | 19.775 | 5.288 | 0.086 | 0.101 | 0.094 | 0.049 | 0.086 | 0.101 | 4 |
27 | 0.019 | 0.030 | 0.312 | 8.664 | 27.919 | 0.126 | 0.219 | 0.080 | 0.055 | 0.126 | 0.219 | 4 |
28 | 0.024 | 0.021 | 0.357 | 4.805 | 29.623 | 0.009 | 0.469 | 0.056 | 0.041 | 0.009 | 0.469 | 4 |
29 | 0.030 | 0.020 | 0.259 | 32.938 | 28.889 | 0.099 | 0.436 | 0.052 | 0.049 | 0.099 | 0.436 | 4 |
30 | 0.018 | 0.017 | 0.182 | 4.482 | 2.045 | 0.027 | 0.288 | 0.041 | 0.026 | 0.027 | 0.288 | 4 |
31 | 0.028 | 0.026 | 0.164 | 26.525 | 25.949 | 0.117 | 0.084 | 0.058 | 0.035 | 0.117 | 0.084 | 4 |
32 | 0.023 | 0.020 | 0.372 | 39.113 | 5.546 | 0.136 | 0.443 | 0.075 | 0.064 | 0.136 | 0.443 | 4 |
33 | 0.032 | 0.022 | 0.353 | 1.944 | 19.318 | 0.082 | 0.353 | 0.084 | 0.047 | 0.082 | 0.353 | 4 |
34 | 0.029 | 0.031 | 0.110 | 2.429 | 4.162 | 0.059 | 0.432 | 0.026 | 0.056 | 0.059 | 0.432 | 4 |
35 | 0.027 | 0.024 | 0.165 | 47.290 | 21.058 | 0.041 | 0.089 | 0.051 | 0.029 | 0.041 | 0.089 | 4 |
36 | 0.025 | 0.022 | 0.348 | 17.164 | 26.863 | 0.063 | 0.455 | 0.076 | 0.052 | 0.063 | 0.455 | 4 |
37 | 0.017 | 0.024 | 0.361 | 9.553 | 7.454 | 0.027 | 0.054 | 0.103 | 0.029 | 0.027 | 0.054 | 3 |
38 | 0.027 | 0.022 | 0.222 | 46.392 | 21.362 | 0.167 | 0.320 | 0.051 | 0.051 | 0.167 | 0.320 | 4 |
39 | 0.028 | 0.018 | 0.247 | 21.006 | 7.505 | 0.115 | 0.465 | 0.046 | 0.048 | 0.115 | 0.465 | 4 |
40 | 0.018 | 0.026 | 0.143 | 34.607 | 19.392 | 0.022 | 0.103 | 0.046 | 0.030 | 0.022 | 0.103 | 4 |
41 | 0.021 | 0.033 | 0.203 | 46.859 | 24.756 | 0.139 | 0.184 | 0.068 | 0.049 | 0.139 | 0.184 | 4 |
42 | 0.028 | 0.021 | 0.251 | 22.415 | 11.566 | 0.026 | 0.043 | 0.072 | 0.025 | 0.026 | 0.043 | 4 |
43 | 0.021 | 0.020 | 0.390 | 14.424 | 26.982 | 0.078 | 0.408 | 0.079 | 0.049 | 0.078 | 0.408 | 4 |
44 | 0.018 | 0.017 | 0.113 | 4.843 | 4.594 | 0.037 | 0.277 | 0.028 | 0.026 | 0.037 | 0.277 | 4 |
45 | 0.020 | 0.028 | 0.376 | 2.375 | 17.141 | 0.054 | 0.302 | 0.083 | 0.048 | 0.054 | 0.302 | 4 |
46 | 0.029 | 0.023 | 0.125 | 2.299 | 25.985 | 0.052 | 0.456 | 0.024 | 0.044 | 0.052 | 0.456 | 4 |
47 | 0.028 | 0.033 | 0.353 | 34.218 | 7.959 | 0.010 | 0.207 | 0.081 | 0.042 | 0.010 | 0.207 | 4 |
48 | 0.018 | 0.033 | 0.222 | 38.289 | 27.674 | 0.134 | 0.430 | 0.046 | 0.072 | 0.134 | 0.430 | 4 |
49 | 0.030 | 0.022 | 0.272 | 25.403 | 9.279 | 0.021 | 0.315 | 0.054 | 0.035 | 0.021 | 0.315 | 4 |
50 | 0.023 | 0.030 | 0.119 | 2.163 | 27.532 | 0.135 | 0.126 | 0.051 | 0.037 | 0.135 | 0.126 | 4 |
Sampled parameters and calibration condition | Calibration results | |||||||||||
| ||||||||||||
1 | 0.033 | 0.030 | 0.136 | 25.388 | 7.775 | 0.100 | 0.429 | 0.040 | 0.057 | 0.100 | 0.429 | 4 |
2 | 0.026 | 0.025 | 0.294 | 25.452 | 10.004 | 0.061 | 0.433 | 0.057 | 0.053 | 0.061 | 0.433 | 4 |
3 | 0.022 | 0.032 | 0.268 | 9.053 | 18.416 | 0.065 | 0.333 | 0.066 | 0.055 | 0.065 | 0.333 | 4 |
4 | 0.027 | 0.022 | 0.159 | 30.943 | 15.777 | 0.107 | 0.286 | 0.042 | 0.038 | 0.107 | 0.286 | 4 |
5 | 0.020 | 0.032 | 0.184 | 35.273 | 19.612 | 0.025 | 0.484 | 0.033 | 0.063 | 0.025 | 0.484 | 4 |
6 | 0.019 | 0.017 | 0.363 | 46.871 | 29.933 | 0.081 | 0.050 | 0.105 | 0.029 | 0.081 | 0.050 | 4 |
7 | 0.021 | 0.026 | 0.164 | 35.976 | 10.444 | 0.050 | 0.437 | 0.034 | 0.050 | 0.050 | 0.437 | 4 |
8 | 0.017 | 0.023 | 0.149 | 45.299 | 27.869 | 0.013 | 0.349 | 0.031 | 0.035 | 0.013 | 0.349 | 4 |
9 | 0.018 | 0.022 | 0.122 | 2.960 | 2.103 | 0.161 | 0.067 | 0.050 | 0.031 | 0.161 | 0.067 | 4 |
10 | 0.020 | 0.025 | 0.210 | 47.955 | 15.737 | 0.099 | 0.044 | 0.072 | 0.034 | 0.099 | 0.044 | 4 |
11 | 0.018 | 0.021 | 0.120 | 22.432 | 23.321 | 0.114 | 0.424 | 0.028 | 0.042 | 0.114 | 0.424 | 4 |
12 | 0.032 | 0.023 | 0.155 | 27.625 | 4.781 | 0.107 | 0.234 | 0.044 | 0.037 | 0.107 | 0.234 | 4 |
13 | 0.029 | 0.027 | 0.324 | 36.150 | 6.654 | 0.087 | 0.303 | 0.063 | 0.051 | 0.087 | 0.303 | 4 |
14 | 0.018 | 0.020 | 0.144 | 29.338 | 26.770 | 0.008 | 0.357 | 0.027 | 0.032 | 0.008 | 0.357 | 4 |
15 | 0.019 | 0.032 | 0.377 | 42.820 | 16.166 | 0.168 | 0.403 | 0.084 | 0.086 | 0.168 | 0.403 | 4 |
16 | 0.028 | 0.017 | 0.126 | 15.874 | 24.707 | 0.160 | 0.237 | 0.041 | 0.030 | 0.160 | 0.237 | 4 |
17 | 0.021 | 0.024 | 0.275 | 14.494 | 1.718 | 0.097 | 0.111 | 0.111 | 0.047 | 0.097 | 0.111 | 4 |
18 | 0.032 | 0.026 | 0.254 | 14.086 | 11.617 | 0.085 | 0.231 | 0.053 | 0.044 | 0.085 | 0.231 | 4 |
19 | 0.020 | 0.030 | 0.300 | 18.883 | 1.811 | 0.022 | 0.358 | 0.054 | 0.051 | 0.022 | 0.358 | 4 |
20 | 0.024 | 0.024 | 0.274 | 5.479 | 9.004 | 0.161 | 0.068 | 0.091 | 0.043 | 0.161 | 0.068 | 4 |
21 | 0.033 | 0.024 | 0.149 | 26.541 | 10.778 | 0.003 | 0.325 | 0.032 | 0.035 | 0.003 | 0.325 | 4 |
22 | 0.024 | 0.031 | 0.173 | 0.848 | 2.736 | 0.019 | 0.206 | 0.050 | 0.040 | 0.019 | 0.206 | 4 |
23 | 0.017 | 0.020 | 0.147 | 35.029 | 14.683 | 0.102 | 0.117 | 0.046 | 0.028 | 0.102 | 0.117 | 4 |
24 | 0.026 | 0.030 | 0.121 | 23.521 | 10.510 | 0.114 | 0.340 | 0.036 | 0.049 | 0.114 | 0.340 | 4 |
25 | 0.029 | 0.030 | 0.169 | 35.260 | 8.151 | 0.122 | 0.496 | 0.035 | 0.070 | 0.122 | 0.496 | 4 |
26 | 0.028 | 0.031 | 0.357 | 19.775 | 5.288 | 0.086 | 0.101 | 0.094 | 0.049 | 0.086 | 0.101 | 4 |
27 | 0.019 | 0.030 | 0.312 | 8.664 | 27.919 | 0.126 | 0.219 | 0.080 | 0.055 | 0.126 | 0.219 | 4 |
28 | 0.024 | 0.021 | 0.357 | 4.805 | 29.623 | 0.009 | 0.469 | 0.056 | 0.041 | 0.009 | 0.469 | 4 |
29 | 0.030 | 0.020 | 0.259 | 32.938 | 28.889 | 0.099 | 0.436 | 0.052 | 0.049 | 0.099 | 0.436 | 4 |
30 | 0.018 | 0.017 | 0.182 | 4.482 | 2.045 | 0.027 | 0.288 | 0.041 | 0.026 | 0.027 | 0.288 | 4 |
31 | 0.028 | 0.026 | 0.164 | 26.525 | 25.949 | 0.117 | 0.084 | 0.058 | 0.035 | 0.117 | 0.084 | 4 |
32 | 0.023 | 0.020 | 0.372 | 39.113 | 5.546 | 0.136 | 0.443 | 0.075 | 0.064 | 0.136 | 0.443 | 4 |
33 | 0.032 | 0.022 | 0.353 | 1.944 | 19.318 | 0.082 | 0.353 | 0.084 | 0.047 | 0.082 | 0.353 | 4 |
34 | 0.029 | 0.031 | 0.110 | 2.429 | 4.162 | 0.059 | 0.432 | 0.026 | 0.056 | 0.059 | 0.432 | 4 |
35 | 0.027 | 0.024 | 0.165 | 47.290 | 21.058 | 0.041 | 0.089 | 0.051 | 0.029 | 0.041 | 0.089 | 4 |
36 | 0.025 | 0.022 | 0.348 | 17.164 | 26.863 | 0.063 | 0.455 | 0.076 | 0.052 | 0.063 | 0.455 | 4 |
37 | 0.017 | 0.024 | 0.361 | 9.553 | 7.454 | 0.027 | 0.054 | 0.103 | 0.029 | 0.027 | 0.054 | 3 |
38 | 0.027 | 0.022 | 0.222 | 46.392 | 21.362 | 0.167 | 0.320 | 0.051 | 0.051 | 0.167 | 0.320 | 4 |
39 | 0.028 | 0.018 | 0.247 | 21.006 | 7.505 | 0.115 | 0.465 | 0.046 | 0.048 | 0.115 | 0.465 | 4 |
40 | 0.018 | 0.026 | 0.143 | 34.607 | 19.392 | 0.022 | 0.103 | 0.046 | 0.030 | 0.022 | 0.103 | 4 |
41 | 0.021 | 0.033 | 0.203 | 46.859 | 24.756 | 0.139 | 0.184 | 0.068 | 0.049 | 0.139 | 0.184 | 4 |
42 | 0.028 | 0.021 | 0.251 | 22.415 | 11.566 | 0.026 | 0.043 | 0.072 | 0.025 | 0.026 | 0.043 | 4 |
43 | 0.021 | 0.020 | 0.390 | 14.424 | 26.982 | 0.078 | 0.408 | 0.079 | 0.049 | 0.078 | 0.408 | 4 |
44 | 0.018 | 0.017 | 0.113 | 4.843 | 4.594 | 0.037 | 0.277 | 0.028 | 0.026 | 0.037 | 0.277 | 4 |
45 | 0.020 | 0.028 | 0.376 | 2.375 | 17.141 | 0.054 | 0.302 | 0.083 | 0.048 | 0.054 | 0.302 | 4 |
46 | 0.029 | 0.023 | 0.125 | 2.299 | 25.985 | 0.052 | 0.456 | 0.024 | 0.044 | 0.052 | 0.456 | 4 |
47 | 0.028 | 0.033 | 0.353 | 34.218 | 7.959 | 0.010 | 0.207 | 0.081 | 0.042 | 0.010 | 0.207 | 4 |
48 | 0.018 | 0.033 | 0.222 | 38.289 | 27.674 | 0.134 | 0.430 | 0.046 | 0.072 | 0.134 | 0.430 | 4 |
49 | 0.030 | 0.022 | 0.272 | 25.403 | 9.279 | 0.021 | 0.315 | 0.054 | 0.035 | 0.021 | 0.315 | 4 |
50 | 0.023 | 0.030 | 0.119 | 2.163 | 27.532 | 0.135 | 0.126 | 0.051 | 0.037 | 0.135 | 0.126 | 4 |
Symbol | Range | References | ||
Model Parameters | ||||
Background mortality rate (/yr) | | [11] | ||
Recruitment rate into the population (/yr) | | | ||
Rate of HIV progression (/yr) | | 0.1-0.4 | [11] | |
Calibration Conditions | ||||
HIV prevalence at endemic equilibrium | | 0.3-17 | [18] | |
Peak HIV incidence | | 10%-50% of | ||
HIV prevalence at time of peak HIV incidence | | 5%-95% of | ||
Calibration Parameters | ||||
Initial value of transmission term (/yr) | | determined by calibration procedure | ||
Location of transmission term | | determined by calibration procedure | ||
Shape of transmission term | | determined by calibration procedure |
Symbol | Range | References | ||
Model Parameters | ||||
Background mortality rate (/yr) | | [11] | ||
Recruitment rate into the population (/yr) | | | ||
Rate of HIV progression (/yr) | | 0.1-0.4 | [11] | |
Calibration Conditions | ||||
HIV prevalence at endemic equilibrium | | 0.3-17 | [18] | |
Peak HIV incidence | | 10%-50% of | ||
HIV prevalence at time of peak HIV incidence | | 5%-95% of | ||
Calibration Parameters | ||||
Initial value of transmission term (/yr) | | determined by calibration procedure | ||
Location of transmission term | | determined by calibration procedure | ||
Shape of transmission term | | determined by calibration procedure |
Sampled parameters and calibration condition | Calibration results | ||||||||||||
| | | | | | | | ||||||
1 | 0.031 | 0.028 | 0.306 | 0.095 | 0.016 | 0.011 | 224.91 | 1.22212E+01 | 0.2 | 0.095 | 0.016 | 0.011 | 2 |
2 | 0.017 | 0.027 | 0.115 | 0.054 | 0.017 | 0.036 | 0.54 | 2.80696E+09 | 7.2 | 0.054 | 0.017 | 0.036 | 2 |
3 | 0.031 | 0.022 | 0.171 | 0.015 | 0.007 | 0.006 | 1.82 | 2.22785E+04 | 2.1 | 0.015 | 0.007 | 0.006 | 2 |
4 | 0.024 | 0.026 | 0.372 | 0.023 | 0.009 | 0.020 | 0.46 | 1.09674E+42 | 25.5 | 0.023 | 0.009 | 0.020 | 3 |
5 | 0.032 | 0.032 | 0.192 | 0.168 | 0.066 | 0.151 | 0.52 | 1.91294E+33 | 42.7 | 0.168 | 0.066 | 0.152 | 3 |
6 | 0.022 | 0.023 | 0.102 | 0.120 | 0.044 | 0.105 | 0.48 | 1.30078E+32 | 34.4 | 0.120 | 0.044 | 0.104 | 3 |
7 | 0.031 | 0.018 | 0.307 | 0.093 | 0.013 | 0.021 | 15.58 | 1.04219E+01 | 0.3 | 0.093 | 0.013 | 0.021 | 2 |
8 | 0.024 | 0.017 | 0.224 | 0.143 | 0.057 | 0.037 | 3.86 | 3.28571E+01 | 1.1 | 0.143 | 0.057 | 0.039 | 2 |
9 | 0.027 | 0.033 | 0.124 | 0.160 | 0.042 | 0.013 | 62.63 | 1.27961E+01 | 0.3 | 0.160 | 0.042 | 0.014 | 2 |
10 | 0.032 | 0.023 | 0.215 | 0.105 | 0.029 | 0.097 | 0.34 | 1.15023E+57 | 58.1 | 0.105 | 0.029 | 0.096 | 3 |
11 | 0.023 | 0.020 | 0.138 | 0.110 | 0.049 | 0.064 | 0.97 | 2.69922E+05 | 5.2 | 0.110 | 0.049 | 0.066 | 2 |
12 | 0.032 | 0.024 | 0.393 | 0.102 | 0.044 | 0.068 | 0.80 | 3.07050E+06 | 6.3 | 0.102 | 0.044 | 0.070 | 2 |
13 | 0.031 | 0.018 | 0.199 | 0.074 | 0.013 | 0.055 | 0.27 | 5.60380E+09 | 8.5 | 0.074 | 0.013 | 0.055 | 2 |
14 | 0.026 | 0.023 | 0.386 | 0.049 | 0.019 | 0.018 | 2.04 | 2.41472E+02 | 1.5 | 0.049 | 0.019 | 0.018 | 2 |
15 | 0.033 | 0.032 | 0.364 | 0.138 | 0.067 | 0.073 | 1.32 | 1.62810E+03 | 3.3 | 0.138 | 0.067 | 0.071 | 2 |
16 | 0.018 | 0.032 | 0.378 | 0.055 | 0.010 | 0.024 | 1.11 | 4.61171E+01 | 1.0 | 0.055 | 0.010 | 0.024 | 2 |
17 | 0.027 | 0.019 | 0.254 | 0.170 | 0.064 | 0.075 | 1.36 | 1.83155E+02 | 2.4 | 0.170 | 0.064 | 0.075 | 2 |
18 | 0.018 | 0.025 | 0.223 | 0.062 | 0.028 | 0.051 | 0.62 | 5.34456E+22 | 18.6 | 0.062 | 0.028 | 0.050 | 3 |
19 | 0.025 | 0.017 | 0.177 | 0.147 | 0.058 | 0.051 | 2.07 | 9.90795E+01 | 1.7 | 0.147 | 0.058 | 0.049 | 2 |
20 | 0.017 | 0.032 | 0.337 | 0.013 | 0.005 | 0.012 | 0.43 | 2.57848E+149 | 79.2 | 0.013 | 0.005 | 0.012 | 3 |
21 | 0.031 | 0.028 | 0.367 | 0.083 | 0.016 | 0.050 | 0.48 | 1.12025E+03 | 2.7 | 0.083 | 0.016 | 0.050 | 2 |
22 | 0.017 | 0.023 | 0.213 | 0.157 | 0.035 | 0.030 | 6.57 | 1.27404E+01 | 0.6 | 0.157 | 0.035 | 0.028 | 2 |
23 | 0.023 | 0.022 | 0.278 | 0.124 | 0.051 | 0.010 | 104.17 | 1.40918E+01 | 0.3 | 0.124 | 0.051 | 0.009 | 2 |
24 | 0.020 | 0.018 | 0.280 | 0.044 | 0.013 | 0.025 | 0.69 | 2.06649E+05 | 3.7 | 0.044 | 0.013 | 0.025 | 2 |
25 | 0.027 | 0.023 | 0.234 | 0.169 | 0.018 | 0.084 | 0.54 | 1.16327E+01 | 1.0 | 0.169 | 0.018 | 0.084 | 2 |
26 | 0.025 | 0.017 | 0.112 | 0.041 | 0.008 | 0.018 | 0.69 | 5.50369E+03 | 2.4 | 0.041 | 0.008 | 0.018 | 2 |
27 | 0.021 | 0.030 | 0.135 | 0.146 | 0.067 | 0.094 | 0.90 | 9.15850E+05 | 6.6 | 0.146 | 0.067 | 0.093 | 2 |
28 | 0.026 | 0.022 | 0.237 | 0.076 | 0.014 | 0.021 | 2.34 | 2.52938E+01 | 0.8 | 0.076 | 0.014 | 0.021 | 2 |
29 | 0.021 | 0.025 | 0.245 | 0.105 | 0.038 | 0.092 | 0.47 | 2.27510E+28 | 28.8 | 0.105 | 0.038 | 0.091 | 3 |
30 | 0.021 | 0.030 | 0.277 | 0.119 | 0.057 | 0.106 | 0.62 | 2.40327E+33 | 35.8 | 0.119 | 0.057 | 0.107 | 3 |
31 | 0.024 | 0.017 | 0.382 | 0.092 | 0.017 | 0.013 | 137.54 | 1.16973E+01 | 0.2 | 0.092 | 0.017 | 0.013 | 2 |
32 | 0.017 | 0.033 | 0.111 | 0.097 | 0.020 | 0.034 | 1.18 | 9.80157E+01 | 1.5 | 0.097 | 0.020 | 0.034 | 2 |
33 | 0.023 | 0.019 | 0.150 | 0.041 | 0.013 | 0.038 | 0.36 | 3.52296E+107 | 77.2 | 0.041 | 0.013 | 0.039 | 3 |
34 | 0.026 | 0.019 | 0.115 | 0.065 | 0.020 | 0.058 | 0.38 | 9.88557E+45 | 38.4 | 0.065 | 0.020 | 0.058 | 3 |
35 | 0.018 | 0.029 | 0.133 | 0.123 | 0.039 | 0.046 | 1.45 | 1.60470E+02 | 1.9 | 0.123 | 0.039 | 0.047 | 2 |
36 | 0.018 | 0.023 | 0.212 | 0.128 | 0.048 | 0.049 | 1.72 | 1.44867E+02 | 1.9 | 0.128 | 0.048 | 0.050 | 2 |
37 | 0.029 | 0.022 | 0.194 | 0.131 | 0.036 | 0.021 | 9.28 | 1.59178E+01 | 0.6 | 0.131 | 0.036 | 0.021 | 2 |
38 | 0.023 | 0.029 | 0.113 | 0.147 | 0.030 | 0.120 | 0.30 | 2.46362E+14 | 17.0 | 0.147 | 0.030 | 0.120 | 2 |
39 | 0.030 | 0.030 | 0.132 | 0.093 | 0.041 | 0.071 | 0.66 | 5.17855E+13 | 12.9 | 0.093 | 0.041 | 0.071 | 2 |
40 | 0.028 | 0.032 | 0.370 | 0.034 | 0.007 | 0.031 | 0.23 | 6.39613E+38 | 26.6 | 0.034 | 0.007 | 0.031 | 2 |
41 | 0.026 | 0.028 | 0.264 | 0.012 | 0.002 | 0.010 | 0.26 | 7.91021E+25 | 13.5 | 0.012 | 0.002 | 0.010 | 2 |
42 | 0.022 | 0.021 | 0.139 | 0.038 | 0.018 | 0.003 | 60.79 | 2.99343E+01 | 0.4 | 0.038 | 0.018 | 0.003 | 2 |
43 | 0.029 | 0.025 | 0.175 | 0.131 | 0.044 | 0.017 | 16.96 | 1.61755E+01 | 0.5 | 0.131 | 0.044 | 0.015 | 2 |
44 | 0.031 | 0.019 | 0.163 | 0.061 | 0.013 | 0.042 | 0.38 | 6.60195E+08 | 7.0 | 0.061 | 0.013 | 0.041 | 2 |
45 | 0.021 | 0.017 | 0.238 | 0.141 | 0.053 | 0.106 | 0.61 | 7.72114E+09 | 11.3 | 0.141 | 0.053 | 0.104 | 2 |
46 | 0.023 | 0.027 | 0.104 | 0.124 | 0.052 | 0.103 | 0.59 | 1.88292E+20 | 22.0 | 0.124 | 0.052 | 0.105 | 3 |
47 | 0.024 | 0.029 | 0.295 | 0.076 | 0.025 | 0.052 | 0.57 | 9.65496E+07 | 6.9 | 0.076 | 0.024 | 0.053 | 2 |
48 | 0.027 | 0.029 | 0.378 | 0.106 | 0.012 | 0.091 | 0.21 | 2.25508E+02 | 2.7 | 0.106 | 0.012 | 0.091 | 2 |
49 | 0.030 | 0.033 | 0.202 | 0.024 | 0.003 | 0.016 | 0.24 | 6.01293E+05 | 3.5 | 0.024 | 0.003 | 0.016 | 2 |
50 | 0.029 | 0.020 | 0.116 | 0.028 | 0.008 | 0.007 | 2.62 | 2.59513E+02 | 1.2 | 0.028 | 0.008 | 0.007 | 2 |
Sampled parameters and calibration condition | Calibration results | ||||||||||||
| | | | | | | | ||||||
1 | 0.031 | 0.028 | 0.306 | 0.095 | 0.016 | 0.011 | 224.91 | 1.22212E+01 | 0.2 | 0.095 | 0.016 | 0.011 | 2 |
2 | 0.017 | 0.027 | 0.115 | 0.054 | 0.017 | 0.036 | 0.54 | 2.80696E+09 | 7.2 | 0.054 | 0.017 | 0.036 | 2 |
3 | 0.031 | 0.022 | 0.171 | 0.015 | 0.007 | 0.006 | 1.82 | 2.22785E+04 | 2.1 | 0.015 | 0.007 | 0.006 | 2 |
4 | 0.024 | 0.026 | 0.372 | 0.023 | 0.009 | 0.020 | 0.46 | 1.09674E+42 | 25.5 | 0.023 | 0.009 | 0.020 | 3 |
5 | 0.032 | 0.032 | 0.192 | 0.168 | 0.066 | 0.151 | 0.52 | 1.91294E+33 | 42.7 | 0.168 | 0.066 | 0.152 | 3 |
6 | 0.022 | 0.023 | 0.102 | 0.120 | 0.044 | 0.105 | 0.48 | 1.30078E+32 | 34.4 | 0.120 | 0.044 | 0.104 | 3 |
7 | 0.031 | 0.018 | 0.307 | 0.093 | 0.013 | 0.021 | 15.58 | 1.04219E+01 | 0.3 | 0.093 | 0.013 | 0.021 | 2 |
8 | 0.024 | 0.017 | 0.224 | 0.143 | 0.057 | 0.037 | 3.86 | 3.28571E+01 | 1.1 | 0.143 | 0.057 | 0.039 | 2 |
9 | 0.027 | 0.033 | 0.124 | 0.160 | 0.042 | 0.013 | 62.63 | 1.27961E+01 | 0.3 | 0.160 | 0.042 | 0.014 | 2 |
10 | 0.032 | 0.023 | 0.215 | 0.105 | 0.029 | 0.097 | 0.34 | 1.15023E+57 | 58.1 | 0.105 | 0.029 | 0.096 | 3 |
11 | 0.023 | 0.020 | 0.138 | 0.110 | 0.049 | 0.064 | 0.97 | 2.69922E+05 | 5.2 | 0.110 | 0.049 | 0.066 | 2 |
12 | 0.032 | 0.024 | 0.393 | 0.102 | 0.044 | 0.068 | 0.80 | 3.07050E+06 | 6.3 | 0.102 | 0.044 | 0.070 | 2 |
13 | 0.031 | 0.018 | 0.199 | 0.074 | 0.013 | 0.055 | 0.27 | 5.60380E+09 | 8.5 | 0.074 | 0.013 | 0.055 | 2 |
14 | 0.026 | 0.023 | 0.386 | 0.049 | 0.019 | 0.018 | 2.04 | 2.41472E+02 | 1.5 | 0.049 | 0.019 | 0.018 | 2 |
15 | 0.033 | 0.032 | 0.364 | 0.138 | 0.067 | 0.073 | 1.32 | 1.62810E+03 | 3.3 | 0.138 | 0.067 | 0.071 | 2 |
16 | 0.018 | 0.032 | 0.378 | 0.055 | 0.010 | 0.024 | 1.11 | 4.61171E+01 | 1.0 | 0.055 | 0.010 | 0.024 | 2 |
17 | 0.027 | 0.019 | 0.254 | 0.170 | 0.064 | 0.075 | 1.36 | 1.83155E+02 | 2.4 | 0.170 | 0.064 | 0.075 | 2 |
18 | 0.018 | 0.025 | 0.223 | 0.062 | 0.028 | 0.051 | 0.62 | 5.34456E+22 | 18.6 | 0.062 | 0.028 | 0.050 | 3 |
19 | 0.025 | 0.017 | 0.177 | 0.147 | 0.058 | 0.051 | 2.07 | 9.90795E+01 | 1.7 | 0.147 | 0.058 | 0.049 | 2 |
20 | 0.017 | 0.032 | 0.337 | 0.013 | 0.005 | 0.012 | 0.43 | 2.57848E+149 | 79.2 | 0.013 | 0.005 | 0.012 | 3 |
21 | 0.031 | 0.028 | 0.367 | 0.083 | 0.016 | 0.050 | 0.48 | 1.12025E+03 | 2.7 | 0.083 | 0.016 | 0.050 | 2 |
22 | 0.017 | 0.023 | 0.213 | 0.157 | 0.035 | 0.030 | 6.57 | 1.27404E+01 | 0.6 | 0.157 | 0.035 | 0.028 | 2 |
23 | 0.023 | 0.022 | 0.278 | 0.124 | 0.051 | 0.010 | 104.17 | 1.40918E+01 | 0.3 | 0.124 | 0.051 | 0.009 | 2 |
24 | 0.020 | 0.018 | 0.280 | 0.044 | 0.013 | 0.025 | 0.69 | 2.06649E+05 | 3.7 | 0.044 | 0.013 | 0.025 | 2 |
25 | 0.027 | 0.023 | 0.234 | 0.169 | 0.018 | 0.084 | 0.54 | 1.16327E+01 | 1.0 | 0.169 | 0.018 | 0.084 | 2 |
26 | 0.025 | 0.017 | 0.112 | 0.041 | 0.008 | 0.018 | 0.69 | 5.50369E+03 | 2.4 | 0.041 | 0.008 | 0.018 | 2 |
27 | 0.021 | 0.030 | 0.135 | 0.146 | 0.067 | 0.094 | 0.90 | 9.15850E+05 | 6.6 | 0.146 | 0.067 | 0.093 | 2 |
28 | 0.026 | 0.022 | 0.237 | 0.076 | 0.014 | 0.021 | 2.34 | 2.52938E+01 | 0.8 | 0.076 | 0.014 | 0.021 | 2 |
29 | 0.021 | 0.025 | 0.245 | 0.105 | 0.038 | 0.092 | 0.47 | 2.27510E+28 | 28.8 | 0.105 | 0.038 | 0.091 | 3 |
30 | 0.021 | 0.030 | 0.277 | 0.119 | 0.057 | 0.106 | 0.62 | 2.40327E+33 | 35.8 | 0.119 | 0.057 | 0.107 | 3 |
31 | 0.024 | 0.017 | 0.382 | 0.092 | 0.017 | 0.013 | 137.54 | 1.16973E+01 | 0.2 | 0.092 | 0.017 | 0.013 | 2 |
32 | 0.017 | 0.033 | 0.111 | 0.097 | 0.020 | 0.034 | 1.18 | 9.80157E+01 | 1.5 | 0.097 | 0.020 | 0.034 | 2 |
33 | 0.023 | 0.019 | 0.150 | 0.041 | 0.013 | 0.038 | 0.36 | 3.52296E+107 | 77.2 | 0.041 | 0.013 | 0.039 | 3 |
34 | 0.026 | 0.019 | 0.115 | 0.065 | 0.020 | 0.058 | 0.38 | 9.88557E+45 | 38.4 | 0.065 | 0.020 | 0.058 | 3 |
35 | 0.018 | 0.029 | 0.133 | 0.123 | 0.039 | 0.046 | 1.45 | 1.60470E+02 | 1.9 | 0.123 | 0.039 | 0.047 | 2 |
36 | 0.018 | 0.023 | 0.212 | 0.128 | 0.048 | 0.049 | 1.72 | 1.44867E+02 | 1.9 | 0.128 | 0.048 | 0.050 | 2 |
37 | 0.029 | 0.022 | 0.194 | 0.131 | 0.036 | 0.021 | 9.28 | 1.59178E+01 | 0.6 | 0.131 | 0.036 | 0.021 | 2 |
38 | 0.023 | 0.029 | 0.113 | 0.147 | 0.030 | 0.120 | 0.30 | 2.46362E+14 | 17.0 | 0.147 | 0.030 | 0.120 | 2 |
39 | 0.030 | 0.030 | 0.132 | 0.093 | 0.041 | 0.071 | 0.66 | 5.17855E+13 | 12.9 | 0.093 | 0.041 | 0.071 | 2 |
40 | 0.028 | 0.032 | 0.370 | 0.034 | 0.007 | 0.031 | 0.23 | 6.39613E+38 | 26.6 | 0.034 | 0.007 | 0.031 | 2 |
41 | 0.026 | 0.028 | 0.264 | 0.012 | 0.002 | 0.010 | 0.26 | 7.91021E+25 | 13.5 | 0.012 | 0.002 | 0.010 | 2 |
42 | 0.022 | 0.021 | 0.139 | 0.038 | 0.018 | 0.003 | 60.79 | 2.99343E+01 | 0.4 | 0.038 | 0.018 | 0.003 | 2 |
43 | 0.029 | 0.025 | 0.175 | 0.131 | 0.044 | 0.017 | 16.96 | 1.61755E+01 | 0.5 | 0.131 | 0.044 | 0.015 | 2 |
44 | 0.031 | 0.019 | 0.163 | 0.061 | 0.013 | 0.042 | 0.38 | 6.60195E+08 | 7.0 | 0.061 | 0.013 | 0.041 | 2 |
45 | 0.021 | 0.017 | 0.238 | 0.141 | 0.053 | 0.106 | 0.61 | 7.72114E+09 | 11.3 | 0.141 | 0.053 | 0.104 | 2 |
46 | 0.023 | 0.027 | 0.104 | 0.124 | 0.052 | 0.103 | 0.59 | 1.88292E+20 | 22.0 | 0.124 | 0.052 | 0.105 | 3 |
47 | 0.024 | 0.029 | 0.295 | 0.076 | 0.025 | 0.052 | 0.57 | 9.65496E+07 | 6.9 | 0.076 | 0.024 | 0.053 | 2 |
48 | 0.027 | 0.029 | 0.378 | 0.106 | 0.012 | 0.091 | 0.21 | 2.25508E+02 | 2.7 | 0.106 | 0.012 | 0.091 | 2 |
49 | 0.030 | 0.033 | 0.202 | 0.024 | 0.003 | 0.016 | 0.24 | 6.01293E+05 | 3.5 | 0.024 | 0.003 | 0.016 | 2 |
50 | 0.029 | 0.020 | 0.116 | 0.028 | 0.008 | 0.007 | 2.62 | 2.59513E+02 | 1.2 | 0.028 | 0.008 | 0.007 | 2 |
Symbol | Range | References | |
Model Parameters | |||
Background mortality rate (/yr) | [11] | ||
Recruitment rate into the population (/yr) | | ||
Rate of HIV progression (/yr) | 0.1-0.4 | [11] | |
Calibration Conditions | |||
HIV prevalence at endemic equilibrium | 0.3-17 | [18] | |
HSV-2 prevalence at endemic equilibrium | 4-50 | [2,16,22,20] | |
Peak HIV incidence | 10%-50% of | ||
HIV prevalence at time of peak HIV incidence | 5%-95% of | ||
Calibration Parameters | |||
Initial value of HIV transmission term (/yr) | determined by calibration procedure | ||
Initial value of HSV-2 transmission term (/yr) | determined by calibration procedure | ||
Location of transmission term | determined by calibration procedure | ||
Shape of transmission term | determined by calibration procedure |
Symbol | Range | References | |
Model Parameters | |||
Background mortality rate (/yr) | [11] | ||
Recruitment rate into the population (/yr) | | ||
Rate of HIV progression (/yr) | 0.1-0.4 | [11] | |
Calibration Conditions | |||
HIV prevalence at endemic equilibrium | 0.3-17 | [18] | |
HSV-2 prevalence at endemic equilibrium | 4-50 | [2,16,22,20] | |
Peak HIV incidence | 10%-50% of | ||
HIV prevalence at time of peak HIV incidence | 5%-95% of | ||
Calibration Parameters | |||
Initial value of HIV transmission term (/yr) | determined by calibration procedure | ||
Initial value of HSV-2 transmission term (/yr) | determined by calibration procedure | ||
Location of transmission term | determined by calibration procedure | ||
Shape of transmission term | determined by calibration procedure |
Sampled parameters and calibration condition | Calibration results | ||||||||||||||||
| | | | | | | | | | | | | |||||
1 | 0.019 | 0.030 | 0.245 | 0.066 | 0.278 | 0.017 | 0.007 | 27.363 | 24.30 | 1.57188E+01 | 0.3 | 0.066 | 0.278 | 0.023 | 0.010 | 2 | 4 |
2 | 0.033 | 0.019 | 0.222 | 0.073 | 0.499 | 0.026 | 0.032 | 0.623 | 0.82 | 1.33110E+03 | 2.4 | 0.073 | 0.499 | 0.037 | 0.033 | 2 | 4 |
3 | 0.018 | 0.021 | 0.119 | 0.105 | 0.422 | 0.012 | 0.028 | 0.980 | 1.32 | 2.00261E+01 | 0.8 | 0.105 | 0.422 | 0.017 | 0.030 | 2 | 4 |
4 | 0.027 | 0.027 | 0.183 | 0.149 | 0.314 | 0.025 | 0.022 | 9.194 | 9.80 | 1.09897E+01 | 0.4 | 0.149 | 0.314 | 0.036 | 0.028 | 2 | 4 |
5 | 0.027 | 0.021 | 0.271 | 0.087 | 0.125 | 0.026 | 0.059 | 0.462 | 0.20 | 1.78937E+07 | 6.6 | 0.087 | 0.125 | 0.033 | 0.059 | 2 | 4 |
6 | 0.027 | 0.020 | 0.366 | 0.013 | 0.383 | 0.004 | 0.010 | 0.267 | 0.14 | 1.04947E+22 | 11.5 | 0.013 | 0.383 | 0.005 | 0.010 | 2 | 4 |
7 | 0.027 | 0.017 | 0.101 | 0.035 | 0.475 | 0.011 | 0.014 | 0.726 | 1.09 | 5.92861E+03 | 2.2 | 0.035 | 0.475 | 0.014 | 0.014 | 2 | 4 |
8 | 0.027 | 0.025 | 0.127 | 0.102 | 0.408 | 0.042 | 0.072 | 0.407 | 0.59 | 1.09128E+10 | 9.7 | 0.102 | 0.408 | 0.063 | 0.073 | 2 | 4 |
9 | 0.027 | 0.033 | 0.171 | 0.042 | 0.456 | 0.013 | 0.009 | 2.812 | 4.86 | 5.02452E+01 | 0.8 | 0.042 | 0.456 | 0.017 | 0.010 | 2 | 4 |
10 | 0.022 | 0.027 | 0.188 | 0.088 | 0.167 | 0.030 | 0.032 | 1.258 | 0.95 | 1.90229E+02 | 1.7 | 0.088 | 0.167 | 0.045 | 0.035 | 2 | 4 |
11 | 0.017 | 0.024 | 0.393 | 0.068 | 0.354 | 0.012 | 0.031 | 0.593 | 0.43 | 4.13872E+01 | 1.1 | 0.068 | 0.354 | 0.016 | 0.031 | 2 | 4 |
12 | 0.022 | 0.021 | 0.132 | 0.108 | 0.446 | 0.022 | 0.086 | 0.145 | 0.25 | 1.00813E+14 | 14.3 | 0.108 | 0.446 | 0.032 | 0.085 | 2 | 4 |
13 | 0.022 | 0.018 | 0.274 | 0.090 | 0.325 | 0.027 | 0.041 | 0.664 | 0.44 | 5.42991E+02 | 2.2 | 0.090 | 0.325 | 0.037 | 0.042 | 2 | 4 |
14 | 0.030 | 0.029 | 0.158 | 0.154 | 0.447 | 0.053 | 0.024 | 5.053 | 8.46 | 1.69047E+01 | 0.7 | 0.154 | 0.447 | 0.078 | 0.026 | 2 | 4 |
15 | 0.020 | 0.021 | 0.315 | 0.099 | 0.064 | 0.032 | 0.087 | 0.349 | 0.15 | 2.83629E+28 | 28.2 | 0.099 | 0.064 | 0.042 | 0.088 | 2 | 4 |
16 | 0.029 | 0.032 | 0.213 | 0.013 | 0.174 | 0.004 | 0.010 | 0.319 | 0.25 | 3.11897E+23 | 12.3 | 0.013 | 0.174 | 0.007 | 0.010 | 2 | 4 |
17 | 0.019 | 0.026 | 0.225 | 0.087 | 0.313 | 0.019 | 0.031 | 0.941 | 0.77 | 6.22601E+01 | 1.3 | 0.087 | 0.313 | 0.026 | 0.031 | 2 | 4 |
18 | 0.017 | 0.021 | 0.251 | 0.092 | 0.265 | 0.013 | 0.027 | 1.891 | 1.09 | 1.44818E+01 | 0.6 | 0.092 | 0.265 | 0.016 | 0.029 | 2 | 4 |
19 | 0.026 | 0.030 | 0.167 | 0.098 | 0.242 | 0.016 | 0.041 | 0.531 | 0.50 | 8.84472E+01 | 1.5 | 0.098 | 0.242 | 0.024 | 0.043 | 2 | 4 |
20 | 0.032 | 0.018 | 0.162 | 0.004 | 0.253 | 0.001 | 0.003 | 0.315 | 0.21 | 1.69847E+39 | 16.4 | 0.004 | 0.253 | 0.002 | 0.004 | 2 | 4 |
21 | 0.023 | 0.018 | 0.317 | 0.114 | 0.205 | 0.050 | 0.024 | 5.369 | 2.61 | 2.49145E+01 | 0.8 | 0.114 | 0.205 | 0.063 | 0.025 | 2 | 4 |
22 | 0.022 | 0.018 | 0.349 | 0.097 | 0.156 | 0.013 | 0.043 | 1.036 | 0.37 | 1.20336E+01 | 0.7 | 0.097 | 0.156 | 0.015 | 0.047 | 2 | 4 |
23 | 0.020 | 0.021 | 0.121 | 0.112 | 0.244 | 0.015 | 0.038 | 0.671 | 0.62 | 4.06640E+01 | 1.2 | 0.112 | 0.244 | 0.023 | 0.041 | 2 | 4 |
24 | 0.021 | 0.022 | 0.275 | 0.131 | 0.207 | 0.044 | 0.109 | 0.321 | 0.22 | 9.01245E+16 | 19.0 | 0.131 | 0.207 | 0.068 | 0.111 | 2 | 4 |
25 | 0.033 | 0.027 | 0.128 | 0.048 | 0.134 | 0.021 | 0.040 | 0.412 | 0.35 | 1.47565E+32 | 24.1 | 0.048 | 0.134 | 0.038 | 0.040 | 2 | 4 |
26 | 0.031 | 0.032 | 0.232 | 0.017 | 0.195 | 0.004 | 0.007 | 1.048 | 0.71 | 1.01842E+03 | 1.5 | 0.017 | 0.195 | 0.006 | 0.007 | 2 | 4 |
27 | 0.032 | 0.032 | 0.183 | 0.163 | 0.278 | 0.022 | 0.141 | 0.132 | 0.12 | 4.93217E+16 | 21.3 | 0.163 | 0.278 | 0.031 | 0.142 | 2 | 4 |
28 | 0.030 | 0.027 | 0.363 | 0.080 | 0.128 | 0.031 | 0.041 | 0.975 | 0.39 | 2.89175E+03 | 2.8 | 0.080 | 0.128 | 0.036 | 0.042 | 2 | 4 |
29 | 0.032 | 0.026 | 0.199 | 0.033 | 0.041 | 0.010 | 0.006 | 6.908 | 3.13 | 4.36917E+01 | 0.7 | 0.033 | 0.041 | 0.011 | 0.006 | 2 | 4 |
30 | 0.017 | 0.026 | 0.211 | 0.018 | 0.071 | 0.004 | 0.006 | 1.130 | 0.53 | 4.52802E+02 | 1.2 | 0.018 | 0.071 | 0.004 | 0.006 | 2 | 4 |
31 | 0.027 | 0.017 | 0.339 | 0.008 | 0.434 | 0.001 | 0.003 | 0.583 | 0.36 | 2.40135E+02 | 1.0 | 0.008 | 0.434 | 0.002 | 0.004 | 2 | 4 |
32 | 0.033 | 0.029 | 0.151 | 0.103 | 0.352 | 0.019 | 0.089 | 0.158 | 0.19 | 1.69030E+26 | 26.4 | 0.103 | 0.352 | 0.028 | 0.090 | 2 | 4 |
33 | 0.026 | 0.027 | 0.150 | 0.111 | 0.363 | 0.051 | 0.074 | 0.471 | 0.63 | 5.48670E+07 | 7.7 | 0.111 | 0.363 | 0.080 | 0.076 | 2 | 4 |
34 | 0.029 | 0.028 | 0.327 | 0.118 | 0.083 | 0.041 | 0.025 | 6.144 | 2.99 | 1.75725E+01 | 0.7 | 0.118 | 0.083 | 0.051 | 0.028 | 2 | 4 |
35 | 0.026 | 0.019 | 0.298 | 0.063 | 0.433 | 0.012 | 0.056 | 0.107 | 0.11 | 8.21837E+39 | 33.2 | 0.063 | 0.433 | 0.017 | 0.057 | 2 | 4 |
36 | 0.019 | 0.028 | 0.222 | 0.102 | 0.162 | 0.022 | 0.018 | 6.609 | 4.04 | 1.50967E+01 | 0.5 | 0.102 | 0.162 | 0.029 | 0.021 | 2 | 4 |
37 | 0.025 | 0.017 | 0.321 | 0.153 | 0.449 | 0.023 | 0.029 | 13.872 | 14.87 | 9.29399E+00 | 0.3 | 0.153 | 0.449 | 0.033 | 0.035 | 3 | 4 |
38 | 0.017 | 0.026 | 0.306 | 0.152 | 0.272 | 0.028 | 0.089 | 0.310 | 0.24 | 2.90089E+02 | 2.8 | 0.152 | 0.272 | 0.039 | 0.090 | 2 | 4 |
39 | 0.021 | 0.028 | 0.220 | 0.027 | 0.130 | 0.009 | 0.015 | 0.748 | 0.41 | 4.01353E+05 | 3.3 | 0.027 | 0.130 | 0.012 | 0.015 | 2 | 4 |
40 | 0.021 | 0.018 | 0.102 | 0.105 | 0.395 | 0.049 | 0.027 | 2.254 | 3.06 | 9.83595E+01 | 1.4 | 0.105 | 0.395 | 0.071 | 0.031 | 2 | 4 |
41 | 0.026 | 0.021 | 0.354 | 0.080 | 0.480 | 0.018 | 0.037 | 0.437 | 0.45 | 1.73014E+02 | 1.8 | 0.080 | 0.480 | 0.025 | 0.039 | 2 | 4 |
42 | 0.017 | 0.029 | 0.170 | 0.124 | 0.043 | 0.031 | 0.107 | 0.315 | 0.17 | 1.61848E+24 | 26.5 | 0.124 | 0.043 | 0.032 | 0.108 | 2 | 4 |
43 | 0.031 | 0.031 | 0.370 | 0.064 | 0.332 | 0.012 | 0.011 | 31.695 | 19.29 | 1.22280E+01 | 0.3 | 0.064 | 0.332 | 0.014 | 0.014 | 2 | 4 |
44 | 0.031 | 0.026 | 0.143 | 0.010 | 0.375 | 0.004 | 0.001 | 54.142 | 84.59 | 3.92541E+01 | 0.4 | 0.010 | 0.375 | 0.006 | 0.001 | 2 | 4 |
45 | 0.021 | 0.024 | 0.244 | 0.098 | 0.287 | 0.014 | 0.019 | 7.851 | 6.15 | 1.13403E+01 | 0.4 | 0.098 | 0.287 | 0.019 | 0.022 | 3 | 4 |
46 | 0.023 | 0.021 | 0.385 | 0.120 | 0.139 | 0.052 | 0.021 | 11.064 | 4.83 | 1.65212E+01 | 0.6 | 0.120 | 0.139 | 0.063 | 0.022 | 2 | 4 |
47 | 0.020 | 0.032 | 0.166 | 0.122 | 0.420 | 0.028 | 0.010 | 36.862 | 65.08 | 1.30911E+01 | 0.3 | 0.122 | 0.420 | 0.040 | 0.012 | 2 | 4 |
48 | 0.024 | 0.025 | 0.323 | 0.152 | 0.235 | 0.029 | 0.101 | 0.260 | 0.18 | 4.59014E+03 | 4.4 | 0.152 | 0.235 | 0.043 | 0.102 | 2 | 4 |
49 | 0.025 | 0.026 | 0.384 | 0.031 | 0.171 | 0.011 | 0.006 | 6.999 | 3.11 | 3.49139E+01 | 0.6 | 0.031 | 0.171 | 0.014 | 0.007 | 2 | 4 |
50 | 0.025 | 0.018 | 0.313 | 0.052 | 0.479 | 0.012 | 0.004 | 165.669 | 157.22 | 1.52477E+01 | 0.2 | 0.052 | 0.479 | 0.014 | 0.006 | 2 | 4 |
Sampled parameters and calibration condition | Calibration results | ||||||||||||||||
| | | | | | | | | | | | | |||||
1 | 0.019 | 0.030 | 0.245 | 0.066 | 0.278 | 0.017 | 0.007 | 27.363 | 24.30 | 1.57188E+01 | 0.3 | 0.066 | 0.278 | 0.023 | 0.010 | 2 | 4 |
2 | 0.033 | 0.019 | 0.222 | 0.073 | 0.499 | 0.026 | 0.032 | 0.623 | 0.82 | 1.33110E+03 | 2.4 | 0.073 | 0.499 | 0.037 | 0.033 | 2 | 4 |
3 | 0.018 | 0.021 | 0.119 | 0.105 | 0.422 | 0.012 | 0.028 | 0.980 | 1.32 | 2.00261E+01 | 0.8 | 0.105 | 0.422 | 0.017 | 0.030 | 2 | 4 |
4 | 0.027 | 0.027 | 0.183 | 0.149 | 0.314 | 0.025 | 0.022 | 9.194 | 9.80 | 1.09897E+01 | 0.4 | 0.149 | 0.314 | 0.036 | 0.028 | 2 | 4 |
5 | 0.027 | 0.021 | 0.271 | 0.087 | 0.125 | 0.026 | 0.059 | 0.462 | 0.20 | 1.78937E+07 | 6.6 | 0.087 | 0.125 | 0.033 | 0.059 | 2 | 4 |
6 | 0.027 | 0.020 | 0.366 | 0.013 | 0.383 | 0.004 | 0.010 | 0.267 | 0.14 | 1.04947E+22 | 11.5 | 0.013 | 0.383 | 0.005 | 0.010 | 2 | 4 |
7 | 0.027 | 0.017 | 0.101 | 0.035 | 0.475 | 0.011 | 0.014 | 0.726 | 1.09 | 5.92861E+03 | 2.2 | 0.035 | 0.475 | 0.014 | 0.014 | 2 | 4 |
8 | 0.027 | 0.025 | 0.127 | 0.102 | 0.408 | 0.042 | 0.072 | 0.407 | 0.59 | 1.09128E+10 | 9.7 | 0.102 | 0.408 | 0.063 | 0.073 | 2 | 4 |
9 | 0.027 | 0.033 | 0.171 | 0.042 | 0.456 | 0.013 | 0.009 | 2.812 | 4.86 | 5.02452E+01 | 0.8 | 0.042 | 0.456 | 0.017 | 0.010 | 2 | 4 |
10 | 0.022 | 0.027 | 0.188 | 0.088 | 0.167 | 0.030 | 0.032 | 1.258 | 0.95 | 1.90229E+02 | 1.7 | 0.088 | 0.167 | 0.045 | 0.035 | 2 | 4 |
11 | 0.017 | 0.024 | 0.393 | 0.068 | 0.354 | 0.012 | 0.031 | 0.593 | 0.43 | 4.13872E+01 | 1.1 | 0.068 | 0.354 | 0.016 | 0.031 | 2 | 4 |
12 | 0.022 | 0.021 | 0.132 | 0.108 | 0.446 | 0.022 | 0.086 | 0.145 | 0.25 | 1.00813E+14 | 14.3 | 0.108 | 0.446 | 0.032 | 0.085 | 2 | 4 |
13 | 0.022 | 0.018 | 0.274 | 0.090 | 0.325 | 0.027 | 0.041 | 0.664 | 0.44 | 5.42991E+02 | 2.2 | 0.090 | 0.325 | 0.037 | 0.042 | 2 | 4 |
14 | 0.030 | 0.029 | 0.158 | 0.154 | 0.447 | 0.053 | 0.024 | 5.053 | 8.46 | 1.69047E+01 | 0.7 | 0.154 | 0.447 | 0.078 | 0.026 | 2 | 4 |
15 | 0.020 | 0.021 | 0.315 | 0.099 | 0.064 | 0.032 | 0.087 | 0.349 | 0.15 | 2.83629E+28 | 28.2 | 0.099 | 0.064 | 0.042 | 0.088 | 2 | 4 |
16 | 0.029 | 0.032 | 0.213 | 0.013 | 0.174 | 0.004 | 0.010 | 0.319 | 0.25 | 3.11897E+23 | 12.3 | 0.013 | 0.174 | 0.007 | 0.010 | 2 | 4 |
17 | 0.019 | 0.026 | 0.225 | 0.087 | 0.313 | 0.019 | 0.031 | 0.941 | 0.77 | 6.22601E+01 | 1.3 | 0.087 | 0.313 | 0.026 | 0.031 | 2 | 4 |
18 | 0.017 | 0.021 | 0.251 | 0.092 | 0.265 | 0.013 | 0.027 | 1.891 | 1.09 | 1.44818E+01 | 0.6 | 0.092 | 0.265 | 0.016 | 0.029 | 2 | 4 |
19 | 0.026 | 0.030 | 0.167 | 0.098 | 0.242 | 0.016 | 0.041 | 0.531 | 0.50 | 8.84472E+01 | 1.5 | 0.098 | 0.242 | 0.024 | 0.043 | 2 | 4 |
20 | 0.032 | 0.018 | 0.162 | 0.004 | 0.253 | 0.001 | 0.003 | 0.315 | 0.21 | 1.69847E+39 | 16.4 | 0.004 | 0.253 | 0.002 | 0.004 | 2 | 4 |
21 | 0.023 | 0.018 | 0.317 | 0.114 | 0.205 | 0.050 | 0.024 | 5.369 | 2.61 | 2.49145E+01 | 0.8 | 0.114 | 0.205 | 0.063 | 0.025 | 2 | 4 |
22 | 0.022 | 0.018 | 0.349 | 0.097 | 0.156 | 0.013 | 0.043 | 1.036 | 0.37 | 1.20336E+01 | 0.7 | 0.097 | 0.156 | 0.015 | 0.047 | 2 | 4 |
23 | 0.020 | 0.021 | 0.121 | 0.112 | 0.244 | 0.015 | 0.038 | 0.671 | 0.62 | 4.06640E+01 | 1.2 | 0.112 | 0.244 | 0.023 | 0.041 | 2 | 4 |
24 | 0.021 | 0.022 | 0.275 | 0.131 | 0.207 | 0.044 | 0.109 | 0.321 | 0.22 | 9.01245E+16 | 19.0 | 0.131 | 0.207 | 0.068 | 0.111 | 2 | 4 |
25 | 0.033 | 0.027 | 0.128 | 0.048 | 0.134 | 0.021 | 0.040 | 0.412 | 0.35 | 1.47565E+32 | 24.1 | 0.048 | 0.134 | 0.038 | 0.040 | 2 | 4 |
26 | 0.031 | 0.032 | 0.232 | 0.017 | 0.195 | 0.004 | 0.007 | 1.048 | 0.71 | 1.01842E+03 | 1.5 | 0.017 | 0.195 | 0.006 | 0.007 | 2 | 4 |
27 | 0.032 | 0.032 | 0.183 | 0.163 | 0.278 | 0.022 | 0.141 | 0.132 | 0.12 | 4.93217E+16 | 21.3 | 0.163 | 0.278 | 0.031 | 0.142 | 2 | 4 |
28 | 0.030 | 0.027 | 0.363 | 0.080 | 0.128 | 0.031 | 0.041 | 0.975 | 0.39 | 2.89175E+03 | 2.8 | 0.080 | 0.128 | 0.036 | 0.042 | 2 | 4 |
29 | 0.032 | 0.026 | 0.199 | 0.033 | 0.041 | 0.010 | 0.006 | 6.908 | 3.13 | 4.36917E+01 | 0.7 | 0.033 | 0.041 | 0.011 | 0.006 | 2 | 4 |
30 | 0.017 | 0.026 | 0.211 | 0.018 | 0.071 | 0.004 | 0.006 | 1.130 | 0.53 | 4.52802E+02 | 1.2 | 0.018 | 0.071 | 0.004 | 0.006 | 2 | 4 |
31 | 0.027 | 0.017 | 0.339 | 0.008 | 0.434 | 0.001 | 0.003 | 0.583 | 0.36 | 2.40135E+02 | 1.0 | 0.008 | 0.434 | 0.002 | 0.004 | 2 | 4 |
32 | 0.033 | 0.029 | 0.151 | 0.103 | 0.352 | 0.019 | 0.089 | 0.158 | 0.19 | 1.69030E+26 | 26.4 | 0.103 | 0.352 | 0.028 | 0.090 | 2 | 4 |
33 | 0.026 | 0.027 | 0.150 | 0.111 | 0.363 | 0.051 | 0.074 | 0.471 | 0.63 | 5.48670E+07 | 7.7 | 0.111 | 0.363 | 0.080 | 0.076 | 2 | 4 |
34 | 0.029 | 0.028 | 0.327 | 0.118 | 0.083 | 0.041 | 0.025 | 6.144 | 2.99 | 1.75725E+01 | 0.7 | 0.118 | 0.083 | 0.051 | 0.028 | 2 | 4 |
35 | 0.026 | 0.019 | 0.298 | 0.063 | 0.433 | 0.012 | 0.056 | 0.107 | 0.11 | 8.21837E+39 | 33.2 | 0.063 | 0.433 | 0.017 | 0.057 | 2 | 4 |
36 | 0.019 | 0.028 | 0.222 | 0.102 | 0.162 | 0.022 | 0.018 | 6.609 | 4.04 | 1.50967E+01 | 0.5 | 0.102 | 0.162 | 0.029 | 0.021 | 2 | 4 |
37 | 0.025 | 0.017 | 0.321 | 0.153 | 0.449 | 0.023 | 0.029 | 13.872 | 14.87 | 9.29399E+00 | 0.3 | 0.153 | 0.449 | 0.033 | 0.035 | 3 | 4 |
38 | 0.017 | 0.026 | 0.306 | 0.152 | 0.272 | 0.028 | 0.089 | 0.310 | 0.24 | 2.90089E+02 | 2.8 | 0.152 | 0.272 | 0.039 | 0.090 | 2 | 4 |
39 | 0.021 | 0.028 | 0.220 | 0.027 | 0.130 | 0.009 | 0.015 | 0.748 | 0.41 | 4.01353E+05 | 3.3 | 0.027 | 0.130 | 0.012 | 0.015 | 2 | 4 |
40 | 0.021 | 0.018 | 0.102 | 0.105 | 0.395 | 0.049 | 0.027 | 2.254 | 3.06 | 9.83595E+01 | 1.4 | 0.105 | 0.395 | 0.071 | 0.031 | 2 | 4 |
41 | 0.026 | 0.021 | 0.354 | 0.080 | 0.480 | 0.018 | 0.037 | 0.437 | 0.45 | 1.73014E+02 | 1.8 | 0.080 | 0.480 | 0.025 | 0.039 | 2 | 4 |
42 | 0.017 | 0.029 | 0.170 | 0.124 | 0.043 | 0.031 | 0.107 | 0.315 | 0.17 | 1.61848E+24 | 26.5 | 0.124 | 0.043 | 0.032 | 0.108 | 2 | 4 |
43 | 0.031 | 0.031 | 0.370 | 0.064 | 0.332 | 0.012 | 0.011 | 31.695 | 19.29 | 1.22280E+01 | 0.3 | 0.064 | 0.332 | 0.014 | 0.014 | 2 | 4 |
44 | 0.031 | 0.026 | 0.143 | 0.010 | 0.375 | 0.004 | 0.001 | 54.142 | 84.59 | 3.92541E+01 | 0.4 | 0.010 | 0.375 | 0.006 | 0.001 | 2 | 4 |
45 | 0.021 | 0.024 | 0.244 | 0.098 | 0.287 | 0.014 | 0.019 | 7.851 | 6.15 | 1.13403E+01 | 0.4 | 0.098 | 0.287 | 0.019 | 0.022 | 3 | 4 |
46 | 0.023 | 0.021 | 0.385 | 0.120 | 0.139 | 0.052 | 0.021 | 11.064 | 4.83 | 1.65212E+01 | 0.6 | 0.120 | 0.139 | 0.063 | 0.022 | 2 | 4 |
47 | 0.020 | 0.032 | 0.166 | 0.122 | 0.420 | 0.028 | 0.010 | 36.862 | 65.08 | 1.30911E+01 | 0.3 | 0.122 | 0.420 | 0.040 | 0.012 | 2 | 4 |
48 | 0.024 | 0.025 | 0.323 | 0.152 | 0.235 | 0.029 | 0.101 | 0.260 | 0.18 | 4.59014E+03 | 4.4 | 0.152 | 0.235 | 0.043 | 0.102 | 2 | 4 |
49 | 0.025 | 0.026 | 0.384 | 0.031 | 0.171 | 0.011 | 0.006 | 6.999 | 3.11 | 3.49139E+01 | 0.6 | 0.031 | 0.171 | 0.014 | 0.007 | 2 | 4 |
50 | 0.025 | 0.018 | 0.313 | 0.052 | 0.479 | 0.012 | 0.004 | 165.669 | 157.22 | 1.52477E+01 | 0.2 | 0.052 | 0.479 | 0.014 | 0.006 | 2 | 4 |
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