Deterministic and Stochastic Schistosomiasis Models with General Incidence

Stanislas Ouaro, Ali Traoré

Laboratoire d’Analyse Mathématique des Equations (LAME), Unité de Formation et de Recherche en Sciences Exactes et Appliquées, Département de Mathématiques, Ouagadougou, Burkina Faso.

DOI: 10.4236/am.2013.412229                

Abstract

In this paper, deterministic and stochastic models for schistosomiasis involving four sub-populations are developed. Conditions are given under which system exhibits thresholds behavior. The disease-free equilibrium is globally asymptotically stable if R₀ < 1 and the unique endemic equilibrium is globally asymptotically stable when R₀ > 1. The populations are computationally simulated under various conditions. Comparisons are made between the deterministic and the stochastic model.

Keywords

Computational Simulation; General Incidence; Reproduction Number; Schistosomiasis Model; Stochastic Differential Equation

Conflicts of Interest

The authors declare no conflicts of interest.

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