Mathematical analysis of population migration and its effects to spread of epidemics

Shangbin  Cui; Meng  Bai

doi:10.3934/dcdsb.2015.20.2819

Article Contents

2015, Volume 20, Issue 9: 2819-2858. Doi: 10.3934/dcdsb.2015.20.2819

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Mathematical analysis of population migration and its effects to spread of epidemics

Shangbin Cui^1, and
Meng Bai^2,

1.
Department of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong 510275
2.
School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061

Received: May 31, 2014

Revised: April 30, 2015

Published: October 2015

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Abstract

In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does not have apparent connection with the population density. We call such models as population migration models and migration epidemics models, respectively. We first apply the theories of positive operators and positive semigroups to make systematic investigation to asymptotic behavior of solutions of the population migration models as time goes to infinity, and next use such results to study asymptotic behavior of solutions of the migration epidemics models as time goes to infinity. Some interesting properties of solutions of these models are obtained.

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Mathematics Subject Classification: Primary: 37N25; Secondary: 92D25, 92D30.

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