一类具变系数交错扩散的登革热模型

Abstract

Abstract:

To describe the mutual diffusion phenomenon between human and mosquitoes in the spread and control of dengue fever, we introduce more complex heterogeneous cross-diffusion into the dengue fever model, and explore the impact of cross-diffusion on its dynamics. In view of the contagion risk threshold, we are devoted to analyzing the existence and non-existence of coexistence solution for the steady state. The findings show that if the contagion risk threshold is greater than one associated with some conditions, this scenario is disadvantage to the control of dengue fever, as it will lead to the coexistence of the viruses carried by human and by mosquitoes. Some epidemiological explanations are presented finally.

Key words: Dengue model, Heterogeneous cross-diffusion, Coexistence solution, Contagion risk threshold

CLC Number:

O175.21

Min Zhu,Mengli Liu. A Dengue Fever Model Incorporating Heterogeneous Cross-Diffusion[J].Acta mathematica scientia,Series A, 2022, 42(1): 201-215.

Trendmd

References 32

1	郭鹏娟, 郭钜旋, 王国玲. 不同血清型登革病毒复合感染现状及防控挑战. 中国热带医学, 2018, 18: 99- 102
	Guo P J , Guo J X , Wang G L . The status of co-infection with multiple Dengue virus serotypes and the challenge to disease control. China Tropical Medicine, 2018, 18: 99- 102
2	Alto B W , Juliano S A . Temperature effects on the dynamics of Aedes albopictus (Diptera: Culicidae) populations in the laboratory. J Med Entomol, 2001, 38: 548- 556 doi: 10.1603/0022-2585-38.4.548
3	孟凤霞, 王义冠, 冯磊, 刘起勇. 我国登革热疫情防控与媒介伊蚊的综合治理. 中国媒介生物学及控制杂志, 2015, 26: 4- 10 doi: 10.11853/j.issn.1003.4692.2015.01.002
	Meng F X , Wang Y G , Feng L , Liu Q Y . Review on dengue prevention and control and integrated mosquito management in China. Chinese Journal of Vector Biology and Control, 2015, 26: 4- 10 doi: 10.11853/j.issn.1003.4692.2015.01.002
4	Keeling M J , Rohani P . Modeling Infectious Diseases in Humans and Animals. Princeton, NJ: Princeton University Press, 2008
5	王双明, 樊馨蔓, 张明军, 梁俊荣. 具周期性潜伏期的SEIR传染病模型的动力学. 数学物理学报, 2020, 40A (2): 527- 539 doi: 10.3969/j.issn.1003-3998.2020.02.023
	Wang S M , Fan X M , Zhang M J , Liang J R . The dynamics of an SEIR epidemic model with time-periodic latent period. Acta Math Sci, 2020, 40A (2): 527- 539 doi: 10.3969/j.issn.1003-3998.2020.02.023
6	韩祥临, 汪维刚, 莫嘉琪. 流行性病毒传播生态动力学系统. 数学物理学报, 2019, 39A (1): 200- 208 doi: 10.3969/j.issn.1003-3998.2019.01.019
	Han X L , Wang W G , Mo J Q . Bionomics dynamic system for epidemic virus transmission. Acta Math Sci, 2019, 39A (1): 200- 208 doi: 10.3969/j.issn.1003-3998.2019.01.019
7	Esteva L , Vargas C . Analysis of a dengue disease transmission model. Math Biosci, 1998, 150: 131- 151 doi: 10.1016/S0025-5564(98)10003-2
8	Feng Z L , Velasco-Hernández J X . Competitive exclusion in a vector-host model for the dengue fever. J Math Biol, 1997, 35: 523- 544 doi: 10.1007/s002850050064
9	Zhang X H , Tang S Y , Cheke R A , et al. Models to assess the effects of non-identical sex ratio augmentations of Wolbachia-carrying mosquitoes on the control of dengue disease. Math Biosci, 2018, 299: 58- 72 doi: 10.1016/j.mbs.2018.03.003
10	Champagne C , Cazelles B . Comparison of stochastic and deterministic frameworks in dengue modelling. Math Biosci, 2019, 310: 1- 12 doi: 10.1016/j.mbs.2019.01.010
11	Wang W D , Zhao X Q . A nonlocal and time-delayed reaction-diffusion model of dengue transmission. SIAM J Appl Math, 2011, 71: 147- 168 doi: 10.1137/090775890
12	Zhang L , Wang S M . A time-periodic and reaction-diffusion Dengue fever model with extrinsic incubation period and crowding effects. Nonlinear Anal: Real World Appl, 2020, 51: 102988 doi: 10.1016/j.nonrwa.2019.102988
13	Vaidya N K , Li X P , Wang F B . Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics. Discrete Contin Dyn Syst (Ser B), 2019, 24: 321- 349
14	Zhu M , Lin Z G . The impact of human activity on the risk index and spatial spreading of dengue fever. Nonlinear Anal: Real World Appl, 2018, 39: 424- 450 doi: 10.1016/j.nonrwa.2017.07.007
15	Shigesada N , Kawasaki K , Teramoto E . Spatial segregation of interacting species. J Theor Biol, 1979, 79: 83- 99 doi: 10.1016/0022-5193(79)90258-3
16	Lou Y , Tao Y S , Winkler M . Nonexistence of nonconstant steady-state solutions inatriangular cross-diffusion model. J Differential Equations, 2017, 262: 5160- 5178 doi: 10.1016/j.jde.2017.01.017
17	Jia Y F , Wu J H , Xu H K . Positive solutions of a Lotka-Volterra competition model with cross-diffusion. Comput Math Appl, 2014, 68: 1220- 1228 doi: 10.1016/j.camwa.2014.08.016
18	Zhao H Y , Zhang Q J , Zhu L H . The spaial dynamics of a zebrafish model with cross-diffusions. Math Biosci Eng, 2017, 14: 1035- 1054 doi: 10.3934/mbe.2017054
19	Cai Y L , Wang W M . Stability and Hopf bifurcation of the stationary solutions to an epidemic model with cross-diffusion. Comput Math Appl, 2015, 70: 1906- 1920 doi: 10.1016/j.camwa.2015.08.003
20	Zhu M , Lin Z G , Zhang Q Y . Coexistence of a cross-diffusion dengue fever model in a heterogeneous environment. Comput Math Appl, 2018, 75: 1004- 1015 doi: 10.1016/j.camwa.2017.10.033
21	Gubler D J . Cities spawn epidemic dengue virues. Nat Med, 2004, 10: 129- 130 doi: 10.1038/nm0204-129
22	van den Driessche P , Watmough J . Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci, 2002, 180: 29- 48 doi: 10.1016/S0025-5564(02)00108-6
23	Bendahmane M , Langlais M . A reaction-diffusion system with cross-diffusion modeling the spread of an epidemic disease. J Evol Equ, 2010, 10: 883- 904 doi: 10.1007/s00028-010-0074-y
24	Allen L J S , Bolker B M , Lou Y , et al. Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Discrete Contin Dyn Syst Ser A, 2008, 21: 1- 20 doi: 10.3934/dcds.2008.21.1
25	Zhao X Q . Dynamical Systems in Population Biology. New York: Springer, 2017,
26	Álvarez-Caudevilla P , Du Y H , Peng R . Qualitative analysis of a cooperative reaction-diffusion system in a spatiotemporally degenerate environment. SIAM J Math Anal, 2014, 46: 499- 531 doi: 10.1137/13091628X
27	Pao C V . Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion. Nonlinear Anal, 2005, 60: 1197- 1217 doi: 10.1016/j.na.2004.10.008
28	Neuhauser C . Mathematical challenges in spatial ecology. Notices Amer Math Soc, 2001, 48: 1304- 1314
29	Ni W J , Shi J P , Wang M X . Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model. J Differential Equations, 2018, 264: 6891- 6932 doi: 10.1016/j.jde.2018.02.002
30	Ding W W , Peng R , Wei L . The diffusive logistic model with a free boundary in a heterogeneous time-periodic environment. J Differential Equations, 2017, 263: 2736- 2779 doi: 10.1016/j.jde.2017.04.013
31	Ge J , Kim K I , Lin Z G , et al. A SIS reaction-diffusion-advection model in a low-risk and high-risk domain. J Differential Equations, 2015, 259: 5486- 5509 doi: 10.1016/j.jde.2015.06.035
32	Zhu M , Lin Z G . Modeling the transmission of dengue fever with limited medical resources and self-protection. Discrete Contin Dyn Syst (Ser B), 2018, 23: 957- 974

A Dengue Fever Model Incorporating Heterogeneous Cross-Diffusion

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 32

Related Articles 1

Metrics

Comments

Recommended 0