MATHEMATICAL MODELLING OF THE SPREAD AND TREATMEANT OF LASSA FEVER

Abstract

In this work we formulated and analyzed a mathematical model of the spread and treatment of Lassa fever. The model is a system of first order Ordinary Differential Equations, in which the human population is divided into six mutually exclusive compartments namely; Susceptible Humans (SH), Exposed humans(EH), Asymptomatic Infected humans (AH), Symptomatic infected humans (IH) , Treated humans (TH) and Recovered humans (RH). And the reservoir population is subdivided into two mutually exclusive compartments namely; susceptible reservoir (SR) and Infected Reservoir (IR). The equilibrium states of the model were obtained and their local stabilities were analyzed by using Jacobian matrix approach coupled with Routh-Hurwitz condition. We also analyzed the global stability of the disease-free-equilibrium using Castillo-Chavez, Feng and Huang approach. The result shows that the disease-free-equilibrium state is both locally and globally asymptotically stable since it satisfies the aforementioned criteria. The result of the numerical simulation shows that at high treatment rate, the number of recovered individuals increases and the virus can be eradicated completely.