# Modeling metapopulation dynamics of HIV epidemic on a linear lattice with nearest neighbour coupling

## DOI:

https://doi.org/10.14419/ijamr.v5i1.5544## Published:

2016-03-02## Keywords:

Coupling Strength, Isolation, Metapopulation, Reproductive ratio, Synchronization.## Abstract

Many mathematical models for the spread of infectious diseases in a population assume homogeneous mixing, but due to spatial distribution, there exist distinct patches with unique disease dispersion dynamics, especially if between patch mixing due to travel and migration is limited. In this paper, three levels of disease status in a - patch metapopulation was studied using a simple SIR-HIV epidemic model in a one dimensional nearest neighbour coupling lattice. The basic reproductive ratio , which is a function of coupling strength , is shown to affect stability characteristics of equilibrium points. The disease free equilibrium (DFE) is globally asymptotically stable irrespective of the value of but the stability of the endemic equilibrium point (EEP) depends on the coupling strength . It was found that at the critical value of coupling strength , the subpopulations dynamics are synchronized while for the subpopulation dynamics are independent. Patch isolation strategy for the control of HIV dispersion requires a critical coupling strength of . This interaction restriction reduces to values less than one, and the disease will be eliminated, making isolation effective. Demographic and epidemiological parameters of Vihiga County in Kenya were used in the study.

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