A DIFFUSIVE SVEIR EPIDEMIC MODEL WITH TIME DELAY AND GENERAL INCIDENCE

doi:10.1007/s10473-021-0421-9

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (4): 1385-1404.doi: 10.1007/s10473-021-0421-9

• 论文 • 上一篇

A DIFFUSIVE SVEIR EPIDEMIC MODEL WITH TIME DELAY AND GENERAL INCIDENCE

周金玲, 马新生, 杨瑜, 张同华

1. Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023, China;
2. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China;
3. Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia

收稿日期:2020-03-23 修回日期:2020-10-01 出版日期:2021-08-25 发布日期:2021-09-01
通讯作者: Yu YANG E-mail:yangyu@lixin.edu.cn
作者简介:Jinling ZHOU,E-mail:jlzhou@amss.ac.cn; Xinsheng MA,E-mail:xsma@zisu.edu.cn; Yu YANG,E-mail:yangyu@lixin.edu.cn;Tonghua ZHANG,E-mail:tonghuazhang@swin.edu.au

A DIFFUSIVE SVEIR EPIDEMIC MODEL WITH TIME DELAY AND GENERAL INCIDENCE

Jinling ZHOU, Xinsheng MA, Yu YANG, Tonghua ZHANG

1. Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023, China;
2. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China;
3. Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia

Received:2020-03-23 Revised:2020-10-01 Online:2021-08-25 Published:2021-09-01
Contact: Yu YANG E-mail:yangyu@lixin.edu.cn

摘要/Abstract

摘要： In this paper, we consider a delayed diffusive SVEIR model with general incidence. We first establish the threshold dynamics of this model. Using a Nonstandard Finite Difference (NSFD) scheme, we then give the discretization of the continuous model. Applying Lyapunov functions, global stability of the equilibria are established. Numerical simulations are presented to validate the obtained results. The prolonged time delay can lead to the elimination of the infectiousness.

关键词: SVEIR model, vaccination, Lyapunov function, nonstandard finite difference method

Abstract: In this paper, we consider a delayed diffusive SVEIR model with general incidence. We first establish the threshold dynamics of this model. Using a Nonstandard Finite Difference (NSFD) scheme, we then give the discretization of the continuous model. Applying Lyapunov functions, global stability of the equilibria are established. Numerical simulations are presented to validate the obtained results. The prolonged time delay can lead to the elimination of the infectiousness.

Key words: SVEIR model, vaccination, Lyapunov function, nonstandard finite difference method

中图分类号:

34F05

周金玲, 马新生, 杨瑜, 张同华. A DIFFUSIVE SVEIR EPIDEMIC MODEL WITH TIME DELAY AND GENERAL INCIDENCE[J]. 数学物理学报(英文版), 2021, 41(4): 1385-1404.

Jinling ZHOU, Xinsheng MA, Yu YANG, Tonghua ZHANG. A DIFFUSIVE SVEIR EPIDEMIC MODEL WITH TIME DELAY AND GENERAL INCIDENCE[J]. Acta mathematica scientia,Series B, 2021, 41(4): 1385-1404.

参考文献

[1] Kribs-Zaleta C M, Velasco-Hernández J X. A simple vaccination model with multiple endemic states. Mathematical Biosciences, 2000, 164(2):183-201
[2] Arino J, McCluskey C C, van den Driess P. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM Journal on Applied Mathematics, 2003, 64(1):260-276
[3] Li J, Ma Z, Zhou Y. Global analysis of SIS epidemic model with a simple vaccination and multiple endemic equilibria. Acta Mathematica Scientia, 2006, 26B(1):83-93
[4] Liu X, Takeuchi Y, Iwami S. SVIR epidemic models with vaccination strategies. Journal of Theoretical Biology, 2008, 253(1):1-11
[5] Li J, Yang Y. SIR-SVS epidemic models with continuous and impulsive vaccination strategies. Journal of Theoretical Biology, 2011, 280(1):108-116
[6] Zhu Q, Hao Y, Ma J, Yu S, Wang Y. Surveillance of hand, foot, and mouth disease in mainland china (2008-2009). Biomedical and Environmental Sciences, 2011, 24(4):349-356
[7] Martcheva M. Avian flu:modeling and implications for control. Journal of Biological Systems, 2014, 22(1):151-175
[8] Wang W, Ruan S. Simulating the SARS outbreak in beijing with limited data. Journal of Theoretical Biology, 2004, 227(3):369-379
[9] Liljeros F, Edling C R, Amaral L A N. Sexual networks:implications for the transmission of sexually transmitted infections. Microbes and Infection, 2003, 5(2):189-196
[10] Liu W M, Levin S A, Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological model. Journal of Mathematical Biology, 1986, 23(2):187-204. 18
[11] Capasso V, Serio G. A generalization of the Kermack-McKendrick deterministic epidemic model. Mathematical Biosciences, 1978, 42(1/2):43-61
[12] Hattaf K, Lashari A A, Louartassi Y, Yousfi N. A delayed SIR epidemic model with general incidence rate. Electronic Journal of Qualitative Theory of Differential Equations, 2013(3):1-9
[13] Wang L, Liu Z, Zhang X. Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence. Applied Mathematics and Computation, 2016, 284:47-65
[14] Hattaf K. Global stability and Hopf bifurcation of a generalized viral infection model with multi-delays and humoral immunity. Physica A:Statal Mechanics and its Applications, 2020, 545:123689
[15] Wang J, Huang G, Takeuchi Y, Liu S. SVEIR epidemiological model with varying infectivity and distributed delays. Mathematical Biosciences and Engineering, 2011, 8(3):875-888
[16] Xu R. Global stability of a delayed epidemic model with latent period and vaccination strategy. Applied Mathematical Modelling, 2012, 36(11):5293-5300
[17] Duan X, Yuan S, Li X. Global stability of an SVIR model with age of vaccination. Applied Mathematics and Computation, 2014, 226:528-540
[18] Meng X, Chen L, Wu B. A delay SIR epidemic model with pulse vaccination and incubation times. Nonlinear Analysis:Real World Applications, 2010, 11(1):88-98
[19] Gao S, Chen L, Nieto J J, Torres A. Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. Vaccine, 2006, 24(35/36):6037-6045
[20] Zhang T, Zhang T Q, Meng X. Stability analysis of a chemostat model with maintenance energy. Applied Mathematics Letters, 2017, 68:1-7
[21] Zhang T, Liu X, Meng X, Zhang T Q. Spatio-temporal dynamics near the steady state of a planktonic system. Computers and Mathematics with Applications, 2018, 75(12):4490-4504
[22] Hattaf K, Yousfi N. Global stability for reaction-diffusion equations in biology. Computers Mathematics with Applications, 2013, 66(8):1488-1497
[23] Webby R J, Webster R G. Are we ready for pandemic influenza? Science, 2003, 302:1519-1522
[24] Xu Z, Ai C. Traveling waves in a diffusive influenza epidemic model with vaccination. Applied Mathematical Modelling, 2016, 40(15/16):7265-7280
[25] Abdelmalek S, Bendoukha S. Global asymptotic stability of a diffusive SVIR epidemic model with immigration of individuals. Electronic Journal of Differential Equations, 2016, 2016(129/324):1-14
[26] Xu Z, Xu Y, Huang Y. Stability and traveling waves of a vaccination model with nonlinear incidence. Computers and Mathematics with Applications, 2018, 75(2):561-581
[27] Mickens R E. Nonstandard Finite Difference Models of Differential Equations. World Scientific, December 1993
[28] Arenas A J, Morano J A, Cortés J C. Non-standard numerical method for a mathematical model of RSV epidemiological transmission. Computers and Mathematics with Applications, 2008, 56(3):670-678
[29] Hattaf K, Yousfi N. Global properties of a discrete viral infection model with general incidence rate. Mathematical Methods in the Applied Sciences, 2016, 39(5):998-1004
[30] Hattaf K, Yousfi N. A numerical method for delayed partial differential equations describing infectious diseases. Computers and Mathematics with Applications, 2016, 72(11):2741-2750
[31] Liu J, Peng B, Zhang T. Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence. Applied Mathematics Letters, 2015, 39:60-66
[32] Muroya Y, Bellen A, Enatsu Y, Nakata Y. Global stability for a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population. Nonlinear Analysis:Real World Applications, 2013, 13(1):258-274
[33] Qin W, Wang L, Ding X. A non-standard finite difference method for a hepatitis B virus infection model with spatial diffusion. Journal of Difference Equations and Applications, 2014, 20(12):1641-1651
[34] Geng Y, Xu J. Stability preserving NSFD scheme for a multi-group SVIR epidemic model. Mathematical Methods in the Applied Sciences, 2017, 40(13):4917-4927
[35] Ding D, Ma Q, Ding X. A non-standard finite difference scheme for an epidemic model with vaccination. Journal of Difference Equations and Applications, 2013, 19(2):179-190
[36] Yang Y, Zhou J, Ma X, Zhang T. Nonstandard finite difference scheme for a diffusive within-host virus dynamics model with both virus-to-cell and cell-to-cell transmissions. Computers and Mathematics with Applications, 2016, 72(4):1013-1020
[37] Zhou J, Yang Y, Zhang T. Global dynamics of a reaction-diffusion waterborne pathogen model with general incidence rate. Journal of Mathematical Analysis and Applications, 2018, 466(1):835-859
[38] Martin R H, Smith H L. Abstract functional differential equations and reaction-diffusion systems. Transactions of the American Mathematical Society, 1990, 321(1):1-44
[39] Fujimoto T, Ranade R R. Two characterizations of inverse-positive matrices:the Hawkins-Simon condition and the Le Chatelier-Braun principle. The Electronic Journal of Linear Algebra, 2004, 11:59-65

A DIFFUSIVE SVEIR EPIDEMIC MODEL WITH TIME DELAY AND GENERAL INCIDENCE

A DIFFUSIVE SVEIR EPIDEMIC MODEL WITH TIME DELAY AND GENERAL INCIDENCE

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