Global analysis of multi-strains SIS, SIR and MSIR epidemic models

被引：52
作者：
Bichara D. [1 ,2 ]
Iggidr A. [1 ,2 ]
Sallet G. [1 ,2 ]
机构：
[1] INRIA MASAIE Team, INRIA-Nancy Grand Est, Université de Lorraine, Metz
[2] LMAM, UMR CNRS 7122, I.S.G.M.P. Bât A, Ile du Saulcy
来源：
Journal of Applied Mathematics and Computing | 2014年 / 44卷 / 1-2期
关键词：
Boundary equilibria; Competition; Global Stability; Lyapunov methods; Nonlinear dynamical systems;
D O I：
10.1007/s12190-013-0693-x
中图分类号：
学科分类号：
摘要：
We consider SIS, SIR and MSIR models with standard mass action and varying population, with n different pathogen strains of an infectious disease. We also consider the same models with vertical transmission. We prove that under generic conditions a competitive exclusion principle holds. To each strain a basic reproduction ratio can be associated. It corresponds to the case where only this strain exists. The basic reproduction ratio of the complete system is the maximum of each individual basic reproduction ratio. Actually we also define an equivalent threshold for each strain. The winner of the competition is the strain with the maximum threshold. It turns out that this strain is the most virulent, i.e., this is the strain for which the endemic equilibrium gives the minimum population for the susceptible host population. This can be interpreted as a pessimization principle. © 2013 Korean Society for Computational and Applied Mathematics.
引用
收藏
页码：273 / 292
页数：19
相关论文
共 38 条
  • [1] Ackleh A.S., Allen L.J.S., Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size, J. Math. Biol., 47, pp. 153-168, (2003)
  • [2] Ackleh A.S., Allen L.J.S., Competitive exclusion in sis and sir epidemic models with total cross immunity and density-dependent host mortality, Discrete Contin. Dyn. Syst., Ser. B, 5, pp. 175-188, (2005)
  • [3] Amstrong R.A., McGehee R., Competitive exclusion, Am. Nat., 115, pp. 151-170, (1980)
  • [4] Andreasen V., Lin J., Levin S.A., The dynamics of cocirculating influenza strains conferring partial cross-immunity, J. Math. Biol., 35, pp. 825-842, (1997)
  • [5] Andreasen V., Pugliese A., Pathogen coexistence induced by density-dependent host mortality, J. Theor. Biol, pp. 159-165, (1995)
  • [6] Bremermann H., Thieme H.R., A competitive exclusion principle for pathogen virulence, J. Math. Biol, pp. 179-190, (1989)
  • [7] Castillo-Chavez C., Huang W., Li J., Competitive exclusion in gonorrhea models and other sexually transmitted diseases, SIAM J. Appl. Math., 56, pp. 494-508, (1996)
  • [8] Castillo-Chavez C., Huang W., Li J., Competitive exclusion and coexistence of multiple strains in an SIS STD model, SIAM J. Appl. Math., 59, pp. 1790-1811, (1999)
  • [9] Castillo-Chavez C., Thieme H.R., Asymptotically autonomous epidemic models, Analysis of Heterogeneity, Vol. 1: Theory of Epidemics, pp. 33-50, (1995)
  • [10] Dhirasakdanon T., Thieme H.R., Persistence of vertically transmitted parasite strains which protect against more virulent horizontally transmitted strains, Modeling and Dynamics of Infectious Diseases, pp. 187-215, (2009)
1234