The Existence and Stability Analysis of the Equilibria in Lymphatic Filariasis Model

Abstract

In this paper, a mathematical model describing the dynamics of Lymphatic Filariasis epidemics, which involves the interaction of two principal communities of Hosts (Human) and vectors (mosquitoes) is presented. We found a threshold parameter R0, known as the Basic Reproduction Number. This model has two equilibria, disease-free equilibrium and endemic equilibrium. By construction suitable Lyapunov function. We show that the disease-free equilibrium is globally asymptotic stable whenever R0 is less than one and when it is greater than one, the endemic equilibrium is globally asymptotic stable.