Analysis of the deterministic and stochastic epidemic models of filariasis

Résumé

Abstract:

This article proposes two epidemic models : deterministic and stochastic models of Lymphatic filariasis. For the deterministic model, the basic reproduction number is calculated, the disease- free equilibrium of the model is determined and the stability analysed. If the basic reproduction number is less than one, by using the theorem of Varga (1962) and the standard comparison theorem of Laksmikantham et al. (1989), we have shown that the disease-free equilibrium is globally asymp- totically stable; which means that the disease is eliminated. In the stochastic model, a unique global positive solution for the epidemic model is obtained. We have calculated the threshold parameters which govern the extinction or persistence of the disease. The extinction of the epidemic disease is analysed under assumptions. The persistence in the mean of the stochastic model is also established by building appropriate Lyapunov functions.  A comparison of the two models is made. Numerical simulations are carried out to confirm the analytical results.

Keywords: Lymphatic Filariasis; Itô’s formula; Extinction; Persistence in the mean.