Turing instability in a diffusive SIS epidemiological model

作     者：Shaban Aly Houari B. Khenous Fatma Hussien 

作者机构：Department of Mathematics Faculty of Science King Khalid University Abha 9005 Kingdom of Saudi Arabia Department of Mathematics Faculty of Science Assiut University Egypt 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2015年第8卷第1期

页      面：69-79页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 081304[工学-建筑技术科学] 0805[工学-材料科学与工程（可授工学、理学学位）] 080502[工学-材料学] 0813[工学-建筑学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：SIS epidemiological model reaction-diffusion equation diffusive instability Turing instability. 

摘      要：Modeling and simulation of infectious diseases help to predict the likely outcome of an epidemic. In this paper, a spatial susceptible-infective-susceptible （SIS） type of epidemiological disease model with self- and cross-diffusion are investigated. We study the effect of diffusion on the stability of the endemic equilibrium with disease-induced mortality and nonlinear incidence rate, In the absence of diffusion the stationary solution stays stable but becomes unstable with respect to diffusion and that Turing instability takes place. We show that a standard （self-diffusion） system may be either stable or unstable, cross-diffusion response can stabilize an unstable standard system or decrease a ＂ihlring space （the space which the emergence of spatial patterns is holding） compared to the ~lhlring space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges. Numerical simulations are provided to illustrate and extend the theoretical results.