Migration influence on malaria propagation: Coupled Ross-Macdonald models

Abstract

From the classical Ross-Macdonald model of malaria spread we propose a system of coupled differential equations that models the interaction between several population cores. Our model depends on parameters representing human migration rates. We study in detail the case of two population cores. We analyze the dependence of the equilibria of the system with respect to migration parameter. We find three qualitatively different scenarios. We use the technique of reproductive number $R_0$ to study the stability of the disease-free equilibrium. We find that the variation of the migration parameter may force a change of the stability in one of these scenarios.