Mathematical Analysis of a Large Scale Vector SIS Malaria Model in a Patchy Environment

Josephine Wairimu, Sallet Gauthier, Wandera Ogana

INRIA, Metz and University of Lorraine, Lorraine, France.
School of Mathematics, University of Nairobi, Nairobi, Kenya.

DOI: 10.4236/am.2014.513185                

Abstract

We answer the stability question of the large scale SIS model describing transmission of highland malaria in Western Kenya in a patchy environment, formulated in [1]. There are two equilibrium states and their stability depends on the basic reproduction number, R_o [2]. If R_o ≤1, the disease-free steady solution is globally asymptotically stable and the disease always dies out. If R_o >1, there exists a unique endemic equilibrium which is globally stable and the disease persists. Application is done on data from Western Kenya. The age structure reduces the level of infection and the populations settle to the equilibrium faster than in the model without age structure.

Keywords

Highland Malaria, Differentiated Susceptibility and Infectivity, Monotone Dynamical Systems

Conflicts of Interest

The authors declare no conflicts of interest.

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