Restricted migration of infected individuals in epidemic metapopulation model on double graphs

Abstract

When the action range of infected individuals is restricted in a patchy environment, epidemic spreading changes due to the restricted migration. We focus on the effect of the restricted migration of infected individuals to epidemic spreading in a patchy environment. Each individual is either susceptible (S) or infected (I). The restricted migration is represented by the double graphs. We present a metapopulation dynamic model on double graphs; a subpopulation (patch) is represented by a node on the double graphs, a link on the first graph represents a migration path between patches for susceptible individuals, and a link on the second graph represents a migration path between patches for infected individuals. Susceptible and infected individuals move by random walk through a link on the first graph and through a link on the second graph respectively. Two kinds of reaction–diffusion equations are presented as the differential equations for susceptible and infected individuals respectively. To evaluate the infection risk of each patch (node), we obtain the solutions of reaction–diffusion equations numerically. The infected densities change greatly by the restricted migration on double graphs. It is shown that the densities of infected individuals depend highly on the structure of double graphs. In specific double graphs, there exist infected individuals only on the hub (subpopulation with highest degree) and disappear on other subpopulations.