
-
Previous Article
A blow-up result for the chemotaxis system with nonlinear signal production and logistic source
- DCDS-B Home
- This Issue
-
Next Article
Periodic forcing on degenerate Hopf bifurcation
Persistence of mosquito vector and dengue: Impact of seasonal and diurnal temperature variations
1. | Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA, Computational Science Research Center, San Diego State University, San Diego, CA 92182, USA, Viral Information Institute, San Diego State University, San Diego, CA 92182, USA |
2. | Department of Natural Science in the Center for General Education, Chang Gung University, Guishan, Taoyuan 333, Taiwan, Community Medicine Research Center, Chang Gung Memorial Hospital, Keelung Branch, Keelung 204, Taiwan |
Dengue, a mosquito-borne disease, poses a tremendous burden to human health with about 390 million annual dengue infections worldwide. The environmental temperature plays a major role in the mosquito life-cycle as well as the mosquito-human-mosquito dengue transmission cycle. While previous studies have provided useful insights into the understanding of dengue diseases, there is little emphasis put on the role of environmental temperature variation, especially diurnal variation, in the mosquito vector and dengue dynamics. In this study, we develop a mathematical model to investigate the impact of seasonal and diurnal temperature variations on the persistence of mosquito vector and dengue. Importantly, using a threshold dynamical system approach to our model, we formulate the mosquito reproduction number and the infection invasion threshold, which completely determine the global threshold dynamics of mosquito population and dengue transmission, respectively. Our model predicts that both seasonal and diurnal variations of the environmental temperature can be determinant factors for the persistence of mosquito vector and dengue. In general, our numerical estimates of the mosquito reproduction number and the infection invasion threshold show that places with higher diurnal or seasonal temperature variations have a tendency to suffer less from the burden of mosquito population and dengue epidemics. Our results provide novel insights into the theoretical understanding of the role of diurnal temperature, which can be beneficial for the control of mosquito vector and dengue spread.
References:
[1] |
G. Aronsson and R. B. Kellogg,
On a differential equation arising from compartmental analysis, Math. Biosci., 38 (1978), 113-122.
doi: 10.1016/0025-5564(78)90021-4. |
[2] |
N. Bacaër and S. Guernaoui,
The epidemic threshold of vector-borne diseases with seasonality: the case of cutaneous leishmaniasis in Chichaoua, Morocco, J. Math. Biol., 53 (2006), 421-436.
doi: 10.1007/s00285-006-0015-0. |
[3] |
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, 11 (2011), 598-607.
doi: 10.1111/j.1365-3156.2011.02734.x. |
[4] |
S. Bhatt, P. W. Gething, O. J. Brady, J. P. Messina and A. W. Farlow,
The global distribution and burden of dengue, Nature, 496 (2013), 504-507.
doi: 10.1038/nature12060. |
[5] |
O. J. Brady, P. W. Gething, S. Bhatt, J. P. Messina, J. S. Brownstein, et al., Refining the global spatial limits of dengue virus transmission by evidence-based consensus, PLoS Negl. Trop. Dis., 6 (2012), e1760.
doi: 10.1371/journal.pntd.0001760. |
[6] |
G. Chowell, P. Diaz-Dueñas, 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. |
[7] |
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 |
[8] |
T. P. Endy, A. Nisalak, S. Chunsuttiwat, D. H. Libraty and S. Green,
Spatial and temporal circulation of dengue virus serotypes: A prospective study of primary school children in Kamphaeng Phet, Thailand, Am. J. Epidemiol., 156 (2002), 52-59.
doi: 10.1093/aje/kwf006. |
[9] |
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. |
[10] |
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 |
[11] |
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. |
[12] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society Providence, RI, 1988.
doi: 10.1090/surv/025. |
[13] |
M. W. Hirsch,
Systems of differential equations that are competitive or cooperative Ⅱ: Convergence almost everywhere, SIAM J. Math. Anal., 16 (1985), 423-439.
doi: 10.1137/0516030. |
[14] |
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 |
[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, PNAS, 108 (2011), 7460-7465.
doi: 10.1073/pnas.1101377108. |
[18] |
M.-T. Li, G.-Q. Sun, L. Yakob, H.-P. Zhu, Z. Jin and W.-Y. Zhang, The driving force for 2014 dengue outbreak in Guangdong, China, PLoS ONE, 11 (2016), e0166211.
doi: 10.1371/journal.pone.0166211. |
[19] |
L. Liu, X.-Q. Zhao and Y. Zhou,
A tuberculousis model with seasonality, Bull. Math. Biol., 72 (2010), 931-952.
doi: 10.1007/s11538-009-9477-8. |
[20] |
A. Nisalak, T. P. Endy, S. Nimmannitya, S. Kalayanarooj and U. Thisayakorn,
Serotype-specific dengue virus circulation and dengue disease in Bangkok, Thailand from 1973 to 1999, Am. J. Trop. Med. Hyg., 68 (2003), 191-202.
doi: 10.4269/ajtmh.2003.68.191. |
[21] |
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. |
[22] |
K. P. Paaijmans, A. F. Read and M. B. Thomas,
Understanding the link between malaria risk and climate, PNAS, 106 (2009), 13844-13849.
doi: 10.1073/pnas.0903423106. |
[23] |
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 (2014), 225-233. Google Scholar |
[24] |
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 |
[25] |
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. |
[26] |
S. T. R. Pinho, C. P. Ferreira, L. Esteva, F. R. Barreto, V. C. Morato e Silva and M. G. L. Teixeira,
Modelling the dynamics of dengue real epidemics, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 368 (2010), 5679-5693.
doi: 10.1098/rsta.2010.0278. |
[27] |
V. Racloz, R. Ramsey, S. Tong and W. Hu, Surveillance of dengue fever virus: A review of epidemiological models and early warning systems, PLoS Negl. Trop. Dis., 6 (2012), e1648.
doi: 10.1371/journal.pntd.0001648. |
[28] |
D. J. Rogers and S. E. Randolph,
Climate change and vector-borne diseases, Adv. Parasitol., 62 (2006), 345-381.
doi: 10.1016/S0065-308X(05)62010-6. |
[29] |
T. W. Scott, A. C. Morrison, L. H. Lorenz, G. G. Clark and D. Strickman, Longitudinal studies of aedes aegypti (diptera: Culicidae) in Thailand and puerto rico: Population dynamics, J. Med. Entomol., 37 (2000), 77-88. Google Scholar |
[30] |
P. M. Sheppard, W. W. Macdonald, R. J. Tonnand and B. Grab,
The dynamics of an adult population of aedes aegypti in relation to dengue haemorrhagic fever in bangkok, J. Anim. Ecol., 38 (1969), 661-702.
doi: 10.2307/3042. |
[31] |
C. P. Simmons, J. J. Farrar, N. van Vinh Chau and B. Wills, Dengue, J. Vector Borne Dis, 6 (2012), e1648.
doi: 10.1056/NEJMra1110265. |
[32] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, American Mathematical Society Providence, RI, 1995. |
[33] |
H. L. Smith and P. Waltman, The Theory of the Chemostat, CCambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511530043.![]() ![]() |
[34] |
R. W. Sutherst,
Global change and human vulnerability to vector-borne diseases, N. Engl. J. Med., 366 (2012), 1423-1432.
doi: 10.1128/CMR.17.1.136-173.2004. |
[35] |
M. Teurlai, C. E. Menkés, V. Cavarero, N. Degallier, E. Descloux, J.-P. Grangeon, et al., 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] |
N. K. Vaidya, X. Li and F.-B. Wang,
Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 321-349.
doi: 10.3934/dcdsb.2018099. |
[37] |
N. K. Vaidya and L. M. Wahl,
Avian influenza dynamics under periodic environmental conditions, SIAM J. Appl. Math., 75 (2015), 443-467.
doi: 10.1137/140966642. |
[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] |
F.-B. Wang, S.-B. Hsu and W. Wang,
Dynamics of harmful algae with seasonal temperature variations in the cove-main lake, Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), 313-335.
doi: 10.3934/dcdsb.2016.21.313. |
[40] |
W. Wang and X.-Q. Zhao,
Threshold dynamics for compartmental epidemic models in periodic environments, J. Dynam. Differential Equations, 20 (2008), 699-717.
doi: 10.1007/s10884-008-9111-8. |
[41] |
WHO, Dengue Guidelines for Diagnosis, Treatment, Prevention, and Control, TDR: World Health Organization, (2009). Google Scholar |
[42] |
R. E. Woodruff and T. McMichael, Climate change and human health: All affected bit somevvmore than others, Social Alternatives, 23 (2004), 17-22. Google Scholar |
[43] |
H. M. Yang, M. de L. da 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. |
[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 dengue transmission, Epidemiol. Infect., 137 (2009), 1179-1187.
doi: 10.1017/S0950268809002052. |
[45] |
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. |
[46] |
F. Zhang and X.-Q. Zhao,
A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.
doi: 10.1016/j.jmaa.2006.01.085. |
[47] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
[48] |
X.-Q. Zhao,
Asymptotic behavior for asymptotically periodic semiflows with applications, Comm. Appl. Nonlinear Anal., 3 (1996), 43-66.
|
show all references
References:
[1] |
G. Aronsson and R. B. Kellogg,
On a differential equation arising from compartmental analysis, Math. Biosci., 38 (1978), 113-122.
doi: 10.1016/0025-5564(78)90021-4. |
[2] |
N. Bacaër and S. Guernaoui,
The epidemic threshold of vector-borne diseases with seasonality: the case of cutaneous leishmaniasis in Chichaoua, Morocco, J. Math. Biol., 53 (2006), 421-436.
doi: 10.1007/s00285-006-0015-0. |
[3] |
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, 11 (2011), 598-607.
doi: 10.1111/j.1365-3156.2011.02734.x. |
[4] |
S. Bhatt, P. W. Gething, O. J. Brady, J. P. Messina and A. W. Farlow,
The global distribution and burden of dengue, Nature, 496 (2013), 504-507.
doi: 10.1038/nature12060. |
[5] |
O. J. Brady, P. W. Gething, S. Bhatt, J. P. Messina, J. S. Brownstein, et al., Refining the global spatial limits of dengue virus transmission by evidence-based consensus, PLoS Negl. Trop. Dis., 6 (2012), e1760.
doi: 10.1371/journal.pntd.0001760. |
[6] |
G. Chowell, P. Diaz-Dueñas, 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. |
[7] |
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 |
[8] |
T. P. Endy, A. Nisalak, S. Chunsuttiwat, D. H. Libraty and S. Green,
Spatial and temporal circulation of dengue virus serotypes: A prospective study of primary school children in Kamphaeng Phet, Thailand, Am. J. Epidemiol., 156 (2002), 52-59.
doi: 10.1093/aje/kwf006. |
[9] |
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. |
[10] |
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 |
[11] |
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. |
[12] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society Providence, RI, 1988.
doi: 10.1090/surv/025. |
[13] |
M. W. Hirsch,
Systems of differential equations that are competitive or cooperative Ⅱ: Convergence almost everywhere, SIAM J. Math. Anal., 16 (1985), 423-439.
doi: 10.1137/0516030. |
[14] |
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 |
[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, PNAS, 108 (2011), 7460-7465.
doi: 10.1073/pnas.1101377108. |
[18] |
M.-T. Li, G.-Q. Sun, L. Yakob, H.-P. Zhu, Z. Jin and W.-Y. Zhang, The driving force for 2014 dengue outbreak in Guangdong, China, PLoS ONE, 11 (2016), e0166211.
doi: 10.1371/journal.pone.0166211. |
[19] |
L. Liu, X.-Q. Zhao and Y. Zhou,
A tuberculousis model with seasonality, Bull. Math. Biol., 72 (2010), 931-952.
doi: 10.1007/s11538-009-9477-8. |
[20] |
A. Nisalak, T. P. Endy, S. Nimmannitya, S. Kalayanarooj and U. Thisayakorn,
Serotype-specific dengue virus circulation and dengue disease in Bangkok, Thailand from 1973 to 1999, Am. J. Trop. Med. Hyg., 68 (2003), 191-202.
doi: 10.4269/ajtmh.2003.68.191. |
[21] |
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. |
[22] |
K. P. Paaijmans, A. F. Read and M. B. Thomas,
Understanding the link between malaria risk and climate, PNAS, 106 (2009), 13844-13849.
doi: 10.1073/pnas.0903423106. |
[23] |
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 (2014), 225-233. Google Scholar |
[24] |
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 |
[25] |
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. |
[26] |
S. T. R. Pinho, C. P. Ferreira, L. Esteva, F. R. Barreto, V. C. Morato e Silva and M. G. L. Teixeira,
Modelling the dynamics of dengue real epidemics, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 368 (2010), 5679-5693.
doi: 10.1098/rsta.2010.0278. |
[27] |
V. Racloz, R. Ramsey, S. Tong and W. Hu, Surveillance of dengue fever virus: A review of epidemiological models and early warning systems, PLoS Negl. Trop. Dis., 6 (2012), e1648.
doi: 10.1371/journal.pntd.0001648. |
[28] |
D. J. Rogers and S. E. Randolph,
Climate change and vector-borne diseases, Adv. Parasitol., 62 (2006), 345-381.
doi: 10.1016/S0065-308X(05)62010-6. |
[29] |
T. W. Scott, A. C. Morrison, L. H. Lorenz, G. G. Clark and D. Strickman, Longitudinal studies of aedes aegypti (diptera: Culicidae) in Thailand and puerto rico: Population dynamics, J. Med. Entomol., 37 (2000), 77-88. Google Scholar |
[30] |
P. M. Sheppard, W. W. Macdonald, R. J. Tonnand and B. Grab,
The dynamics of an adult population of aedes aegypti in relation to dengue haemorrhagic fever in bangkok, J. Anim. Ecol., 38 (1969), 661-702.
doi: 10.2307/3042. |
[31] |
C. P. Simmons, J. J. Farrar, N. van Vinh Chau and B. Wills, Dengue, J. Vector Borne Dis, 6 (2012), e1648.
doi: 10.1056/NEJMra1110265. |
[32] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, American Mathematical Society Providence, RI, 1995. |
[33] |
H. L. Smith and P. Waltman, The Theory of the Chemostat, CCambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511530043.![]() ![]() |
[34] |
R. W. Sutherst,
Global change and human vulnerability to vector-borne diseases, N. Engl. J. Med., 366 (2012), 1423-1432.
doi: 10.1128/CMR.17.1.136-173.2004. |
[35] |
M. Teurlai, C. E. Menkés, V. Cavarero, N. Degallier, E. Descloux, J.-P. Grangeon, et al., 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] |
N. K. Vaidya, X. Li and F.-B. Wang,
Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 321-349.
doi: 10.3934/dcdsb.2018099. |
[37] |
N. K. Vaidya and L. M. Wahl,
Avian influenza dynamics under periodic environmental conditions, SIAM J. Appl. Math., 75 (2015), 443-467.
doi: 10.1137/140966642. |
[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] |
F.-B. Wang, S.-B. Hsu and W. Wang,
Dynamics of harmful algae with seasonal temperature variations in the cove-main lake, Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), 313-335.
doi: 10.3934/dcdsb.2016.21.313. |
[40] |
W. Wang and X.-Q. Zhao,
Threshold dynamics for compartmental epidemic models in periodic environments, J. Dynam. Differential Equations, 20 (2008), 699-717.
doi: 10.1007/s10884-008-9111-8. |
[41] |
WHO, Dengue Guidelines for Diagnosis, Treatment, Prevention, and Control, TDR: World Health Organization, (2009). Google Scholar |
[42] |
R. E. Woodruff and T. McMichael, Climate change and human health: All affected bit somevvmore than others, Social Alternatives, 23 (2004), 17-22. Google Scholar |
[43] |
H. M. Yang, M. de L. da 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. |
[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 dengue transmission, Epidemiol. Infect., 137 (2009), 1179-1187.
doi: 10.1017/S0950268809002052. |
[45] |
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. |
[46] |
F. Zhang and X.-Q. Zhao,
A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.
doi: 10.1016/j.jmaa.2006.01.085. |
[47] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
[48] |
X.-Q. Zhao,
Asymptotic behavior for asymptotically periodic semiflows with applications, Comm. Appl. Nonlinear Anal., 3 (1996), 43-66.
|







Parameter | Description | Value | Reference |
Fraction of female larvae from eggs | 0.5 (0-1) | [18,26] | |
Per capita biting rate | 0.1 | [6,26] | |
Natural death rate of humans | 4.22 |
Calculated, [16] | |
Intrinsic period | 10 days | [6,16,18,26] | |
Human recovery rate | 0.1 d |
[18,26] | |
In |
9.531 | Data fitting | |
In |
22.55 | Data fitting | |
In |
7.084 | Data fitting | |
In |
0 | Data fitting | |
In |
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 |
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 |
Data fitting | ||
In |
0 | Data fitting | |
In |
1.044 |
Data fitting | |
In |
12.286 | Data fitting | |
In |
32.461 | Data fitting | |
In |
Data fitting |
Parameter | Description | Value | Reference |
Fraction of female larvae from eggs | 0.5 (0-1) | [18,26] | |
Per capita biting rate | 0.1 | [6,26] | |
Natural death rate of humans | 4.22 |
Calculated, [16] | |
Intrinsic period | 10 days | [6,16,18,26] | |
Human recovery rate | 0.1 d |
[18,26] | |
In |
9.531 | Data fitting | |
In |
22.55 | Data fitting | |
In |
7.084 | Data fitting | |
In |
0 | Data fitting | |
In |
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 |
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 |
Data fitting | ||
In |
0 | Data fitting | |
In |
1.044 |
Data fitting | |
In |
12.286 | Data fitting | |
In |
32.461 | Data fitting | |
In |
Data fitting |
[1] |
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 |
[2] |
Rafael Luís, Sandra Mendonça. A note on global stability in the periodic logistic map. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4211-4220. doi: 10.3934/dcdsb.2020094 |
[3] |
Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov. Global asymptotic stability of nonconvex sweeping processes. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1129-1139. doi: 10.3934/dcdsb.2019212 |
[4] |
Michael Grinfeld, Amy Novick-Cohen. Some remarks on stability for a phase field model with memory. Discrete & Continuous Dynamical Systems - A, 2006, 15 (4) : 1089-1117. doi: 10.3934/dcds.2006.15.1089 |
[5] |
Carlos Gutierrez, Nguyen Van Chau. A remark on an eigenvalue condition for the global injectivity of differentiable maps of $R^2$. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 397-402. doi: 10.3934/dcds.2007.17.397 |
[6] |
Bernold Fiedler, Carlos Rocha, Matthias Wolfrum. Sturm global attractors for $S^1$-equivariant parabolic equations. Networks & Heterogeneous Media, 2012, 7 (4) : 617-659. doi: 10.3934/nhm.2012.7.617 |
[7] |
Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016 |
[8] |
Fernando P. da Costa, João T. Pinto, Rafael Sasportes. On the convergence to critical scaling profiles in submonolayer deposition models. Kinetic & Related Models, 2018, 11 (6) : 1359-1376. doi: 10.3934/krm.2018053 |
[9] |
Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817 |
[10] |
V. V. Zhikov, S. E. Pastukhova. Korn inequalities on thin periodic structures. Networks & Heterogeneous Media, 2009, 4 (1) : 153-175. doi: 10.3934/nhm.2009.4.153 |
[11] |
Giovanni Cimatti. Forced periodic solutions for piezoelectric crystals. Communications on Pure & Applied Analysis, 2005, 4 (2) : 475-485. doi: 10.3934/cpaa.2005.4.475 |
[12] |
Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 |
[13] |
Gloria Paoli, Gianpaolo Piscitelli, Rossanno Sannipoli. A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle. Communications on Pure & Applied Analysis, 2021, 20 (1) : 145-158. doi: 10.3934/cpaa.2020261 |
[14] |
Shanshan Chen, Junping Shi, Guohong Zhang. Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 1843-1866. doi: 10.3934/dcdsb.2020042 |
[15] |
Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 |
[16] |
Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277 |
[17] |
Zhi-Min Chen, Philip A. Wilson. Stability of oscillatory gravity wave trains with energy dissipation and Benjamin-Feir instability. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2329-2341. doi: 10.3934/dcdsb.2012.17.2329 |
[18] |
Cécile Carrère, Grégoire Nadin. Influence of mutations in phenotypically-structured populations in time periodic environment. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3609-3630. doi: 10.3934/dcdsb.2020075 |
[19] |
Marcelo Messias. Periodic perturbation of quadratic systems with two infinite heteroclinic cycles. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1881-1899. doi: 10.3934/dcds.2012.32.1881 |
[20] |
Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]