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

TL;DR

This paper develops mathematical models to analyze how population migration influences the spread of epidemics, using operator theory to study long-term behaviors of these models.

Contribution

It introduces a systematic mathematical framework for analyzing population migration and epidemic spread models using positive operator theory.

Findings

Asymptotic behavior of population migration models characterized

Long-term epidemic spread patterns derived from migration dynamics

Properties of solutions indicating stability and spread tendencies

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.