
-
Previous Article
A locking free Reissner-Mindlin element with weak Galerkin rotations
- DCDS-B Home
- This Issue
-
Next Article
Predicting and estimating probability density functions of chaotic systems
Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics
1. | Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA |
2. | Department of Mathematics and Statistics, University of Missouri -Kansas City, Kansas City, MO 64110, USA |
3. | Department of Natural Science in the Center for General Education, Chang Gung University, Guishan, Taoyuan 333, Taiwan |
4. | Community Medicine Research Center, Chang Gung Memorial Hospital, Keelung, Keelung 204, Taiwan |
In recent years, the growing spatial spread of dengue, a mosquito-borne disease, has been a major international public health concern. In this paper, we propose a mathematical model to describe an impact of spatially heterogeneous temperature on the dynamics of dengue epidemics. We first consider homogeneous temperature profiles across space and study sensitivity of the basic reproduction number to the environmental temperature. We then introduce spatially heterogeneous temperature into the model and establish some important properties of dengue dynamics. In particular, we formulate two indices, mosquito reproduction number and infection invasion threshold, which completely determine the global threshold dynamics of the model. We also perform numerical simulations to explore the impact of spatially heterogeneous temperature on the disease dynamics. Our analytical and numerical results reveal that spatial heterogeneity of temperature can have significant impact on expansion of dengue epidemics. Our results, including threshold indices, may provide useful information for effective deployment of spatially targeted interventions.
References:
[1] |
S. Banu, W. Hu, C. Hurst and S. Tong,
Dengue transmission in the Asia-Pacific region: Impact of climate change and socio-environmental factors, Tropical Medicine and International Health, 16 (2011), 598-607.
doi: 10.1111/j.1365-3156.2011.02734.x. |
[2] |
S. Bhatt, P. W. Gething, O. J. Brady, J. P. Messina, A. W. Farlow and C. L. Moyes,
The global distribution and burden of dengue, Nature, 496 (2013), 504-507.
doi: 10.1038/nature12060. |
[3] |
G. Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse and J. M. Hyman,
The Basic Reproduction Number $\mathcal{R}_0$ and Effectiveness of Reactive Interventions during Dengue Epidemics: The 2002 Dengue Outbreak in Easter Island, Chile, Math. Biosci. Eng., 10 (2013), 1455-1474.
doi: 10.3934/mbe.2013.10.1455. |
[4] |
G. Chowell, P. Diaz-Duenas, J. C. Miller, A. Alcazar-Velazco, J. M. Hyman, P. W. Fenimore and C. Castillo-Chavez,
Estimation of the reproduction number of dengue fever from spatial epidemic data, Math. Biosci., 208 (2007), 571-589.
doi: 10.1016/j.mbs.2006.11.011. |
[5] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz,
On the definition and the computation of the basic reproduction ratio $R_0$ in the models for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
|
[6] |
N. C. Dom, Z. A. Latif, A. H. Ahmad, R. Ismail and B. Pradhan, Manifestation of GIS tools for spatial pattern distribution analysis of dengue fever epidemic in the city of Subang Jaya, Malaysia, Environment Asia, 5 (2012), 82-92. Google Scholar |
[7] |
D. A. Focks, E. Daniels, D. G. Haile and J. E. Keesling,
A simulation model of the epidemiology of urban dengue fever: Literature analysis, model development, preliminary validation, and samples of simulation results, Am. J. Trop. Med. Hyg., 53 (1995), 489-506.
doi: 10.4269/ajtmh.1995.53.489. |
[8] |
H. I. Freedman and X.-Q. Zhao,
Global asymptotics in some quasimonotone reaction-diffusion systems with delays, J. Diff. Eq., 137 (1997), 340-362.
doi: 10.1006/jdeq.1997.3264. |
[9] |
A. K. Githeko, S. W. Lindsay, U. E. Confalonieri and J. A. Patz, Climate change and vector-borne diseases: a regional analysis, Bulletin of the World Health Organization, 78 (2000), 1136-1147. Google Scholar |
[10] |
D. J. Gubler,
Epidemic dengue/dengue hemorrhagic fever as a public health, social and economic problem in the 21st century, Trends in Microbiology, 10 (2002), 100-103.
doi: 10.1016/S0966-842X(01)02288-0. |
[11] |
M. J. Hopp and J. A. Foley, Global-scale relationships between climate and the dengue fever vector, Aedes aegypti, Climatic Change, 48 (2001), 441-463. Google Scholar |
[12] |
S. B. Hsu, F. B. Wang and X.-Q. Zhao,
Dynamics of a periodically pulsed bio-reactor model with a hydraulic storage zone, J. Dynamics and Differential Equations, 23 (2011), 817-842.
doi: 10.1007/s10884-011-9224-3. |
[13] |
S. B. Hsu, F. B. Wang and X.-Q. Zhao,
Global dynamics of zooplankton and harmful algae in flowing habitats, J. Differential Equations, 255 (2013), 265-297.
doi: 10.1016/j.jde.2013.04.006. |
[14] |
T. W. Hwang and F.-B. Wang,
Dynamics of a dengue fever transmission model with crowding effect in human population and spatial variation, Discrete and Continuous Dynamical System Series-B, 18 (2013), 147-161.
|
[15] |
S. Karl, N. Halder, J. K. Kelso, S. A. Ritchie and G. J. Milne,
A spatial simulation model for dengue virus infection in urban areas, BMC Infec. Dis., 14 (2014), p447.
doi: 10.1186/1471-2334-14-447. |
[16] |
A. Khan, M. Hassan and M. Imran,
Estimating the basic reproduction number for single-strain dengue fever epidemics, Infectious Diseases of Poverty, 3 (2014), p12.
doi: 10.1186/2049-9957-3-12. |
[17] |
L. Lambrechts, K. P. Paaijmans, T. Fansiri, L. B. Carrington, L. D. Kramer, M. B. Thomas and T. W. Scott,
Impact of daily temperature fluctuations on dengue virus transmission by Aedes aegypti, Proc. Nat. Acad. Sci., 108 (2011), 7460-7465.
doi: 10.1073/pnas.1101377108. |
[18] |
M. Li, G. Sun, L. Yakob, H. Zhu, Z. Jin and W. Zhang,
The Driving Force for 2014 Dengue Outbreak in Guangdong, China, PLoS ONE, 11 (2016), e0166211.
doi: 10.1371/journal.pone.0166211. |
[19] |
Y. Lou and X.-Q. Zhao,
A reaction-diffusion malaria model with incubation period in the vector population, J. Math. Biol., 62 (2011), 543-568.
doi: 10.1007/s00285-010-0346-8. |
[20] |
P. Magal and X.-Q. Zhao,
Global attractors and steady states for uniformly persistent dynamical systems, SIAM. J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[21] |
R. Martin and H. L. Smith,
Abstract functional differential equations and reaction-diffusion systems, Trans. of A.M.S., 321 (1990), 1-44.
|
[22] |
R. D. Nussbaum, Eigenvectors of nonlinear positive operator and the linear Krein-Rutman theorem, in Fixed Point Theory, Lecture Notes in Mathematics (eds. E. Fadell, G. Fournier), 886, Springer, New York/Berlin, (1981), 309–330. |
[23] |
M. Oki and T. Yamamoto,
Climate change, population immunity, and hyperendemicity in the transmission threshold of dengue, PLoS ONE, 7 (2010), e48258.
doi: 10.1371/journal.pone.0048258. |
[24] |
A. Pakhare, Y. Sabde, A. Joshi, R. Jain, A. Kokane and R. Joshi, A study of spatial and meteorological determinants of dengue outbreak in Bhopal City in 2014, PLoS Negl. Trop. Dis., 53 (2016), 225-233. Google Scholar |
[25] |
W. G. Panhuisa, M. Choisyb, X. Xionga, N. S. Choka and P. Akarasewid, Region-wide synchrony and traveling waves of dengue across eight countries in Southeast Asia, Proc. Nat. Acad. Sci., 112 (2015), 13069-13074. Google Scholar |
[26] |
J. A. Patz, D. Campbell-Lendrum, T. Holloway and J. A. Foley,
Impact of regional climate change on human health, Nature, 438 (2005), 310-317.
doi: 10.1038/nature04188. |
[27] |
S. T. R. Pinho, C. P. Ferreira, L. Esteva, F. R. Barreto, V. C. M. e Silva and M. G. L. Teixeira,
Modelling the dynamics of dengue real epidemics, Phil. Trans. R. Soc. A, 368 (2010), 5679-5693.
doi: 10.1098/rsta.2010.0278. |
[28] |
M. H. Protter and M. F. Weinberger, Maximum Principles in Differential Equations, Springer Verlag, 1984.
![]() |
[29] |
V. Racloz, R. Ramsey, S. Tong and W. Hu,
Surveillance of dengue fever virus: A review of epidemiological models and early warning systems, J. Vector Borne Dis., 6 (2012), e1648.
doi: 10.1371/journal.pntd.0001648. |
[30] |
C. P. Simmons, J. J. Farrar, N. van Vinh Chau and B. Wills,
Dengue, N. Engl. J. Med., 366 (2012), 1423-1432.
doi: 10.1056/NEJMra1110265. |
[31] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr 41, American Mathematical Society Providence, RI, 1995. |
[32] |
H. L. Smith and X.-Q. Zhao,
Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[33] |
A. K. Supriatna, Estimating the basic reproduction number of dengue transmission during 2002-2007 outbreaks in Bandung, Indonesia, Dengue Bulletin, 33 (2009), 21-32. Google Scholar |
[34] |
R. W. Sutherst,
Global change and human vulnerability to vector-borne diseases, Clin. Microbiol. Rev., 17 (2004), 136-173.
doi: 10.1128/CMR.17.1.136-173.2004. |
[35] |
M. Teurlai, C. E. Menkes, V. Cavarero, N. Degallier, E. Descloux and J. Grangeon,
Socio-economic and climate factors associated with dengue fever spatial heterogeneity: A worked example in New Caledonia, PLoS Negl. Trop. Dis., 9 (2015), e0004211.
doi: 10.1371/journal.pntd.0004211. |
[36] |
H. R. Thieme,
Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), 755-763.
|
[37] |
H. R. Thieme,
Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM, J. Appl. Math., 70 (2009), 188-211.
doi: 10.1137/080732870. |
[38] |
P. van den Driessche and J. Watmough,
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[39] |
W. Wang and X.-Q. Zhao,
A nonlocal and time-delayed reaction-diffusion model of dengue transmission, SIAM. J Appl. Math., 71 (2011), 147-168.
doi: 10.1137/090775890. |
[40] |
W. Wang and X.-Q. Zhao,
Basic reproduction numbers for reaction-diffusion epidemic models, SIAM J. Appl. Dyn. Syst., 11 (2012), 1652-1673.
doi: 10.1137/120872942. |
[41] |
WHO, Dengue guidelines for giagnosis, treatment, prevention, and control, Geneva: TDR: World Health Organization, 2009. Google Scholar |
[42] |
R. E. Woodruff and T. McMichael, Climate change and human health: All affected bit some more than others, Social Alternatives, 23 (2004), 17-22. Google Scholar |
[43] |
H. M. Yang, M. L. G. Macoris, K. C. Galvani, M. T. M. Andrighetti and D. M. V. Wanderley,
Assessing the effects of temperature on dengue transmission, Epidemiol. Infect., 137 (2009), 1179-1187.
doi: 10.1017/S0950268809002052. |
[44] |
H. M. Yang, M. L. G. Macoris, K. C. Galvani, M. T. M. Andrighetti and D. M. V. Wanderley,
Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue, Epidemiol. Infect., 137 (2009), 1188-1202.
doi: 10.1017/S0950268809002040. |
[45] |
H. M. Yang, M. L. G. Macoris, K. C. Galvani and M. T. M. Andrighetti,
Follow up estimation of Aedes aegypti entomological parameters and mathematical modellings, Biosystems, 103 (2011), 360-371.
doi: 10.1016/j.biosystems.2010.11.002. |
[46] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.
![]() |
show all references
References:
[1] |
S. Banu, W. Hu, C. Hurst and S. Tong,
Dengue transmission in the Asia-Pacific region: Impact of climate change and socio-environmental factors, Tropical Medicine and International Health, 16 (2011), 598-607.
doi: 10.1111/j.1365-3156.2011.02734.x. |
[2] |
S. Bhatt, P. W. Gething, O. J. Brady, J. P. Messina, A. W. Farlow and C. L. Moyes,
The global distribution and burden of dengue, Nature, 496 (2013), 504-507.
doi: 10.1038/nature12060. |
[3] |
G. Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse and J. M. Hyman,
The Basic Reproduction Number $\mathcal{R}_0$ and Effectiveness of Reactive Interventions during Dengue Epidemics: The 2002 Dengue Outbreak in Easter Island, Chile, Math. Biosci. Eng., 10 (2013), 1455-1474.
doi: 10.3934/mbe.2013.10.1455. |
[4] |
G. Chowell, P. Diaz-Duenas, J. C. Miller, A. Alcazar-Velazco, J. M. Hyman, P. W. Fenimore and C. Castillo-Chavez,
Estimation of the reproduction number of dengue fever from spatial epidemic data, Math. Biosci., 208 (2007), 571-589.
doi: 10.1016/j.mbs.2006.11.011. |
[5] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz,
On the definition and the computation of the basic reproduction ratio $R_0$ in the models for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
|
[6] |
N. C. Dom, Z. A. Latif, A. H. Ahmad, R. Ismail and B. Pradhan, Manifestation of GIS tools for spatial pattern distribution analysis of dengue fever epidemic in the city of Subang Jaya, Malaysia, Environment Asia, 5 (2012), 82-92. Google Scholar |
[7] |
D. A. Focks, E. Daniels, D. G. Haile and J. E. Keesling,
A simulation model of the epidemiology of urban dengue fever: Literature analysis, model development, preliminary validation, and samples of simulation results, Am. J. Trop. Med. Hyg., 53 (1995), 489-506.
doi: 10.4269/ajtmh.1995.53.489. |
[8] |
H. I. Freedman and X.-Q. Zhao,
Global asymptotics in some quasimonotone reaction-diffusion systems with delays, J. Diff. Eq., 137 (1997), 340-362.
doi: 10.1006/jdeq.1997.3264. |
[9] |
A. K. Githeko, S. W. Lindsay, U. E. Confalonieri and J. A. Patz, Climate change and vector-borne diseases: a regional analysis, Bulletin of the World Health Organization, 78 (2000), 1136-1147. Google Scholar |
[10] |
D. J. Gubler,
Epidemic dengue/dengue hemorrhagic fever as a public health, social and economic problem in the 21st century, Trends in Microbiology, 10 (2002), 100-103.
doi: 10.1016/S0966-842X(01)02288-0. |
[11] |
M. J. Hopp and J. A. Foley, Global-scale relationships between climate and the dengue fever vector, Aedes aegypti, Climatic Change, 48 (2001), 441-463. Google Scholar |
[12] |
S. B. Hsu, F. B. Wang and X.-Q. Zhao,
Dynamics of a periodically pulsed bio-reactor model with a hydraulic storage zone, J. Dynamics and Differential Equations, 23 (2011), 817-842.
doi: 10.1007/s10884-011-9224-3. |
[13] |
S. B. Hsu, F. B. Wang and X.-Q. Zhao,
Global dynamics of zooplankton and harmful algae in flowing habitats, J. Differential Equations, 255 (2013), 265-297.
doi: 10.1016/j.jde.2013.04.006. |
[14] |
T. W. Hwang and F.-B. Wang,
Dynamics of a dengue fever transmission model with crowding effect in human population and spatial variation, Discrete and Continuous Dynamical System Series-B, 18 (2013), 147-161.
|
[15] |
S. Karl, N. Halder, J. K. Kelso, S. A. Ritchie and G. J. Milne,
A spatial simulation model for dengue virus infection in urban areas, BMC Infec. Dis., 14 (2014), p447.
doi: 10.1186/1471-2334-14-447. |
[16] |
A. Khan, M. Hassan and M. Imran,
Estimating the basic reproduction number for single-strain dengue fever epidemics, Infectious Diseases of Poverty, 3 (2014), p12.
doi: 10.1186/2049-9957-3-12. |
[17] |
L. Lambrechts, K. P. Paaijmans, T. Fansiri, L. B. Carrington, L. D. Kramer, M. B. Thomas and T. W. Scott,
Impact of daily temperature fluctuations on dengue virus transmission by Aedes aegypti, Proc. Nat. Acad. Sci., 108 (2011), 7460-7465.
doi: 10.1073/pnas.1101377108. |
[18] |
M. Li, G. Sun, L. Yakob, H. Zhu, Z. Jin and W. Zhang,
The Driving Force for 2014 Dengue Outbreak in Guangdong, China, PLoS ONE, 11 (2016), e0166211.
doi: 10.1371/journal.pone.0166211. |
[19] |
Y. Lou and X.-Q. Zhao,
A reaction-diffusion malaria model with incubation period in the vector population, J. Math. Biol., 62 (2011), 543-568.
doi: 10.1007/s00285-010-0346-8. |
[20] |
P. Magal and X.-Q. Zhao,
Global attractors and steady states for uniformly persistent dynamical systems, SIAM. J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[21] |
R. Martin and H. L. Smith,
Abstract functional differential equations and reaction-diffusion systems, Trans. of A.M.S., 321 (1990), 1-44.
|
[22] |
R. D. Nussbaum, Eigenvectors of nonlinear positive operator and the linear Krein-Rutman theorem, in Fixed Point Theory, Lecture Notes in Mathematics (eds. E. Fadell, G. Fournier), 886, Springer, New York/Berlin, (1981), 309–330. |
[23] |
M. Oki and T. Yamamoto,
Climate change, population immunity, and hyperendemicity in the transmission threshold of dengue, PLoS ONE, 7 (2010), e48258.
doi: 10.1371/journal.pone.0048258. |
[24] |
A. Pakhare, Y. Sabde, A. Joshi, R. Jain, A. Kokane and R. Joshi, A study of spatial and meteorological determinants of dengue outbreak in Bhopal City in 2014, PLoS Negl. Trop. Dis., 53 (2016), 225-233. Google Scholar |
[25] |
W. G. Panhuisa, M. Choisyb, X. Xionga, N. S. Choka and P. Akarasewid, Region-wide synchrony and traveling waves of dengue across eight countries in Southeast Asia, Proc. Nat. Acad. Sci., 112 (2015), 13069-13074. Google Scholar |
[26] |
J. A. Patz, D. Campbell-Lendrum, T. Holloway and J. A. Foley,
Impact of regional climate change on human health, Nature, 438 (2005), 310-317.
doi: 10.1038/nature04188. |
[27] |
S. T. R. Pinho, C. P. Ferreira, L. Esteva, F. R. Barreto, V. C. M. e Silva and M. G. L. Teixeira,
Modelling the dynamics of dengue real epidemics, Phil. Trans. R. Soc. A, 368 (2010), 5679-5693.
doi: 10.1098/rsta.2010.0278. |
[28] |
M. H. Protter and M. F. Weinberger, Maximum Principles in Differential Equations, Springer Verlag, 1984.
![]() |
[29] |
V. Racloz, R. Ramsey, S. Tong and W. Hu,
Surveillance of dengue fever virus: A review of epidemiological models and early warning systems, J. Vector Borne Dis., 6 (2012), e1648.
doi: 10.1371/journal.pntd.0001648. |
[30] |
C. P. Simmons, J. J. Farrar, N. van Vinh Chau and B. Wills,
Dengue, N. Engl. J. Med., 366 (2012), 1423-1432.
doi: 10.1056/NEJMra1110265. |
[31] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr 41, American Mathematical Society Providence, RI, 1995. |
[32] |
H. L. Smith and X.-Q. Zhao,
Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[33] |
A. K. Supriatna, Estimating the basic reproduction number of dengue transmission during 2002-2007 outbreaks in Bandung, Indonesia, Dengue Bulletin, 33 (2009), 21-32. Google Scholar |
[34] |
R. W. Sutherst,
Global change and human vulnerability to vector-borne diseases, Clin. Microbiol. Rev., 17 (2004), 136-173.
doi: 10.1128/CMR.17.1.136-173.2004. |
[35] |
M. Teurlai, C. E. Menkes, V. Cavarero, N. Degallier, E. Descloux and J. Grangeon,
Socio-economic and climate factors associated with dengue fever spatial heterogeneity: A worked example in New Caledonia, PLoS Negl. Trop. Dis., 9 (2015), e0004211.
doi: 10.1371/journal.pntd.0004211. |
[36] |
H. R. Thieme,
Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), 755-763.
|
[37] |
H. R. Thieme,
Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM, J. Appl. Math., 70 (2009), 188-211.
doi: 10.1137/080732870. |
[38] |
P. van den Driessche and J. Watmough,
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[39] |
W. Wang and X.-Q. Zhao,
A nonlocal and time-delayed reaction-diffusion model of dengue transmission, SIAM. J Appl. Math., 71 (2011), 147-168.
doi: 10.1137/090775890. |
[40] |
W. Wang and X.-Q. Zhao,
Basic reproduction numbers for reaction-diffusion epidemic models, SIAM J. Appl. Dyn. Syst., 11 (2012), 1652-1673.
doi: 10.1137/120872942. |
[41] |
WHO, Dengue guidelines for giagnosis, treatment, prevention, and control, Geneva: TDR: World Health Organization, 2009. Google Scholar |
[42] |
R. E. Woodruff and T. McMichael, Climate change and human health: All affected bit some more than others, Social Alternatives, 23 (2004), 17-22. Google Scholar |
[43] |
H. M. Yang, M. L. G. Macoris, K. C. Galvani, M. T. M. Andrighetti and D. M. V. Wanderley,
Assessing the effects of temperature on dengue transmission, Epidemiol. Infect., 137 (2009), 1179-1187.
doi: 10.1017/S0950268809002052. |
[44] |
H. M. Yang, M. L. G. Macoris, K. C. Galvani, M. T. M. Andrighetti and D. M. V. Wanderley,
Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue, Epidemiol. Infect., 137 (2009), 1188-1202.
doi: 10.1017/S0950268809002040. |
[45] |
H. M. Yang, M. L. G. Macoris, K. C. Galvani and M. T. M. Andrighetti,
Follow up estimation of Aedes aegypti entomological parameters and mathematical modellings, Biosystems, 103 (2011), 360-371.
doi: 10.1016/j.biosystems.2010.11.002. |
[46] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.
![]() |






Parameter | Description | Value | Reference |
fraction of female larvae from eggs | 0.5 (0-1) | [18,27] | |
per capita biting rate | 0.1 | [4,27] | |
Natural death rate of humans | 4.22 |
Calculated, [16] | |
Intrinsic period | 10 days | [4,16,18,27] | |
Human recovery rate | 0.1 d |
[18,27] | |
Diffusion coefficients | - | varied | |
In |
9.531 | Data fitting | |
In |
22.55 | Data fitting | |
In |
7.084 | Data fitting | |
In |
2.914 | Data fitting | |
In |
-0.4986 | Data fitting | |
In |
0.03099 | Data fitting | |
In |
-0.0008236 | Data fitting | |
In |
7.975 |
Data fitting | |
In |
8.044 |
Data fitting | |
In |
11.386 | Data fitting | |
In |
40.1461 | Data fitting | |
In |
0.1901 | Data fitting | |
In |
-0.0134 | Data fitting | |
In |
2.739 |
Data fitting | |
In |
5 |
Data fitting | |
In |
0.0768 | Data fitting | |
In |
18.9871 | Data fitting | |
In |
7 | Data fitting | |
In |
1.044 |
Data fitting | |
In |
12.286 | Data fitting | |
In |
32.461 | Data fitting |
Parameter | Description | Value | Reference |
fraction of female larvae from eggs | 0.5 (0-1) | [18,27] | |
per capita biting rate | 0.1 | [4,27] | |
Natural death rate of humans | 4.22 |
Calculated, [16] | |
Intrinsic period | 10 days | [4,16,18,27] | |
Human recovery rate | 0.1 d |
[18,27] | |
Diffusion coefficients | - | varied | |
In |
9.531 | Data fitting | |
In |
22.55 | Data fitting | |
In |
7.084 | Data fitting | |
In |
2.914 | Data fitting | |
In |
-0.4986 | Data fitting | |
In |
0.03099 | Data fitting | |
In |
-0.0008236 | Data fitting | |
In |
7.975 |
Data fitting | |
In |
8.044 |
Data fitting | |
In |
11.386 | Data fitting | |
In |
40.1461 | Data fitting | |
In |
0.1901 | Data fitting | |
In |
-0.0134 | Data fitting | |
In |
2.739 |
Data fitting | |
In |
5 |
Data fitting | |
In |
0.0768 | Data fitting | |
In |
18.9871 | Data fitting | |
In |
7 | Data fitting | |
In |
1.044 |
Data fitting | |
In |
12.286 | Data fitting | |
In |
32.461 | Data fitting |
[1] |
Zhikun She, Xin Jiang. Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3835-3861. doi: 10.3934/dcdsb.2020259 |
[2] |
Bo Duan, Zhengce Zhang. A reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021067 |
[3] |
Meng-Xue Chang, Bang-Sheng Han, Xiao-Ming Fan. Global dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect. Electronic Research Archive, , () : -. doi: 10.3934/era.2021024 |
[4] |
Wei Wang, Wanbiao Ma, Xiulan Lai. Sufficient conditions for global dynamics of a viral infection model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3989-4011. doi: 10.3934/dcdsb.2020271 |
[5] |
Lorenzo Freddi. Optimal control of the transmission rate in compartmental epidemics. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021007 |
[6] |
Raffaele Folino, Ramón G. Plaza, Marta Strani. Long time dynamics of solutions to $ p $-Laplacian diffusion problems with bistable reaction terms. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3211-3240. doi: 10.3934/dcds.2020403 |
[7] |
Thomas Alazard. A minicourse on the low Mach number limit. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 365-404. doi: 10.3934/dcdss.2008.1.365 |
[8] |
Naeem M. H. Alkoumi, Pedro J. Torres. Estimates on the number of limit cycles of a generalized Abel equation. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 25-34. doi: 10.3934/dcds.2011.31.25 |
[9] |
Mayte Pérez-Llanos, Juan Pablo Pinasco, Nicolas Saintier. Opinion fitness and convergence to consensus in homogeneous and heterogeneous populations. Networks & Heterogeneous Media, 2021, 16 (2) : 257-281. doi: 10.3934/nhm.2021006 |
[10] |
Andrey Kovtanyuk, Alexander Chebotarev, Nikolai Botkin, Varvara Turova, Irina Sidorenko, Renée Lampe. Modeling the pressure distribution in a spatially averaged cerebral capillary network. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021016 |
[11] |
Antonio Rieser. A topological approach to spectral clustering. Foundations of Data Science, 2021, 3 (1) : 49-66. doi: 10.3934/fods.2021005 |
[12] |
Irena PawŃow, Wojciech M. Zajączkowski. Global regular solutions to three-dimensional thermo-visco-elasticity with nonlinear temperature-dependent specific heat. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1331-1372. doi: 10.3934/cpaa.2017065 |
[13] |
Jing Feng, Bin-Guo Wang. An almost periodic Dengue transmission model with age structure and time-delayed input of vector in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3069-3096. doi: 10.3934/dcdsb.2020220 |
[14] |
Rui Wang, Rundong Zhao, Emily Ribando-Gros, Jiahui Chen, Yiying Tong, Guo-Wei Wei. HERMES: Persistent spectral graph software. Foundations of Data Science, 2021, 3 (1) : 67-97. doi: 10.3934/fods.2021006 |
[15] |
Jean-François Biasse. Improvements in the computation of ideal class groups of imaginary quadratic number fields. Advances in Mathematics of Communications, 2010, 4 (2) : 141-154. doi: 10.3934/amc.2010.4.141 |
[16] |
Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175 |
[17] |
Xianjun Wang, Huaguang Gu, Bo Lu. Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron. Electronic Research Archive, , () : -. doi: 10.3934/era.2021023 |
[18] |
Takeshi Saito, Kazuyuki Yagasaki. Chebyshev spectral methods for computing center manifolds. Journal of Computational Dynamics, 2021 doi: 10.3934/jcd.2021008 |
[19] |
Jianping Gao, Shangjiang Guo, Wenxian Shen. Persistence and time periodic positive solutions of doubly nonlocal Fisher-KPP equations in time periodic and space heterogeneous media. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2645-2676. doi: 10.3934/dcdsb.2020199 |
[20] |
Melis Alpaslan Takan, Refail Kasimbeyli. Multiobjective mathematical models and solution approaches for heterogeneous fixed fleet vehicle routing problems. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2073-2095. doi: 10.3934/jimo.2020059 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]