The effect of population dispersal on the spread of a disease

Abstract

The effect of population dispersal among n patches on the spread of a disease is investigated. Population dispersal does not destroy the uniqueness of a disease free equilibrium and its attractivity when the basic reproduction number of a disease R 0 < 1. When R 0 > 1, the uniqueness and global attractivity of the endemic equilibrium can be obtained if dispersal rates of susceptible individuals and infective individuals are the same or very close in each patch. However, numerical calculations show that population dispersal may result in multiple endemic equilibria and even multi-stable equilibria among patches, and also may result in the extinction of a disease, even though it cannot be eradicated in each isolated patch, provided the basic reproduction numbers of isolated patches are not very large.  2005 Elsevier Inc. All rights reserved.

A new approach for designing disease intervention strategies in metapopulation models

“…, r} such that v i = v j i . However, this contradicts (11). Summarizing, we showed that the condition (9) for controllability holds.…”

“…Applying this method, we systematically investigate the intervention strategies of a general SIRS (susceptible-infected-recovered-susceptible) model, that is appropriate for the spread of an infectious disease in a geographically dispersed metapopulation of individuals. While the qualitative properties of metapopulation (patchy) epidemic models have been widely studied in the literature, evaluating the intervention strategies in these models has received less attention (see, for instance, [2,3,6,11,14,18,19] and the references therein). It is particularly challenging to understand the dependence of movement between populations on the reproduction number [2,4,5].…”

Multi-patch deterministic and stochastic models for wildlife diseases

“…In these models, the population size for each species is either assumed to be constant or the per capita birth rate equals the per capita death rate. In other studies, Wang and colleagues [12,14,15] prove global stability of the disease-free and endemic equilibria and verify that the system is uniformly persistent. The Wang and Mulone model [14] is an SIS epidemic model for n patches with a density-dependent births.…”

“…Models that include host demography and stochastic effects are especially important for wildlife diseases due to the wide variability in wildlife population sizes. Deterministic metapopulation models for the spread of disease in a multi-patch system have been studied by others [8][9][10][11][12][13][14][15]. In a review article by Arino and van den Driessche [11], the existence and stability of the disease-free equilibrium or endemic equilibria in a variety of different metapopulation models are summarized.…”

Global stability of a time-delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure

“…In [1], Arino and van den Driessche proposed n-city epidemic models to investigate the effects of inter-city travel on the spatial spread of infectious diseases among cities. In [14], Jin and Wang showed that the n-patch SIS model can be reduced to a monotone system, and the uniqueness and global stability of the endemic equilibrium can be achieved by assuming the dispersal rates of susceptible and infectious individuals are the same. In [21], Li and Shuai investigated an SIR compartmental epidemic model in a patchy environment where individuals in each compartment can travel among n patches.…”