MATHEMATICAL MODEL AND ITS ANALYSIS OF SHIGELLOSIS DISEASE DYNAMICS

Abstract

Shigellosis is one of the most common diarrhea diseases causing lots of morbidity and mortality in developing countries. Shigellosis can occur at any age but it has particularly violence for babies and children. Mathematical modeling is the act of using mathematics to solve real life problems. The objective of this study is to develop and analyze a deterministic mathematical model of Shigellosis disease dynamics by using data from Sude health office. The total population in this model is sub-divided in to six compartments, namely; Susceptible (S), Exposed (E), Carrier(C), Infected (I) ,Recovered(R) and Bacterial concentration (B).Some parameters such as immunity loss rate(α) and recovery rate of the carrier(ω) are also taken from related published articles. The study analyzed the qualitative behavior of the model, like the invariant region, existence of equilibrium points (disease free and endemic equilibrium), basic reproduction number and their stabilities (local as well as global stability).In the study we demonstrated that the disease free equilibrium is locally asymptotically stable if the basic reproduction number is less than 1, and also the endemic equilibrium exists if the basic reproduction number is greater than 1.In order to check the effect of some parameters in the expansion as well as in the control of Shigellosis disease, we used Maple 18 software. The result of numerical simulation shows that reducing contact rate of susceptible to environment(