Impact of population size and movement on the persistence of a two-strain infectious disease

被引:10
作者
Salako, Rachidi B. [1 ]
机构
[1] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA
关键词
Infectious disease models; Reaction-diffusion systems; Asymptotic behavior; SIS EPIDEMIC MODEL; REACTION-DIFFUSION MODEL; POSITIVE STEADY-STATE; ASYMPTOTIC PROFILES; DYNAMICS; RISK;
D O I
10.1007/s00285-022-01842-z
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
This article studies the asymptotic profiles of coexistence endemic equilibrium solutions of a two-strain reaction-diffusion epidemic model with mass-action incidence when the diffusion rates are sufficiently small. We address the question of how the population size and environmental heterogeneity impact the persistence and extinction of the disease when the diffusion rates approach zero. In particular, we show that there is a sharp critical number which depends delicately on the infected groups' diffusion rates and each strain's spatially heterogeneous infection and recovery rates. Moreover, if the total size of the population is kept below this critical number, then the disease could be eradicated by restricting the susceptible hosts' movement . However, if the total population exceeds this critical number, the disease may persist no matter how the movement of the susceptible hosts is controlled. Additionally, our results suggest that the disease may persist if the diffusion rates of the infected groups are kept sufficiently smaller than that of the susceptible group.
引用
收藏
页数:36
相关论文
共 22 条
[1]   COMPETITIVE EXCLUSION AND COEXISTENCE IN A TWO-STRAIN PATHOGEN MODEL WITH DIFFUSION [J].
Ackleh, Azmy S. ;
Deng, Keng ;
Wu, Yixiang .
MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2016, 13 (01) :1-18
[2]  
Allen LJS, 2008, DISCRETE CONT DYN-A, V21, P1
[3]  
[Anonymous], 1989, Geometric theory of semilinear parabolic partial differential equations
[4]   A COMPETITIVE-EXCLUSION PRINCIPLE FOR PATHOGEN VIRULENCE [J].
BREMERMANN, HJ ;
THIEME, HR .
JOURNAL OF MATHEMATICAL BIOLOGY, 1989, 27 (02) :179-190
[5]  
Cantrell R. S., 2003, Spatial ecology via reaction-diffusion equations
[6]   On the effect of lowering population's movement to control the spread of an infectious disease [J].
Castellano, Keoni ;
Salako, Rachidi B. .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 316 :1-27
[7]   Dynamics and asymptotic profiles of steady states of an epidemic model in advective environments [J].
Cui, Renhao ;
Lam, King-Yeung ;
Lou, Yuan .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (04) :2343-2373
[8]   A spatial SIS model in advective heterogeneous environments [J].
Cui, Renhao ;
Lou, Yuan .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (06) :3305-3343
[9]  
de Jong MCM, 1995, EPIDEMIC MODELS THEI
[10]   Dynamics of a susceptible-infected-susceptible epidemic reaction-diffusion model [J].
Deng, Keng ;
Wu, Yixiang .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (05) :929-946