Mathematical Modeling and Stability Analyses of Lassa Fever Disease with the Introduction of the Carrier Compartment

Abstract

In this paper, a new mathematical model which takes into account the human and vector populations together with their interactions during Lassa fever disease transmission was developed. This transmission process is denoted by a seven mutually exclusive compartments for the human and vector populations. The proposed model is used to introduce the incubation period of the disease, a period in which an infected individual is yet to be symptomatic but infectious however, as denoted by the carrier human compartment. This carrier compartment was critically examined for its short and long term effects on the spread and control of the disease. Local and global stability analyses of the equilibrium points of the model was carried out using the first generation matrix approach and the direct Lyapunov method respectively. These analyses showed that the disease free equilibrium point of the developed model is locally asymptotically stable but not globally asymptotically stable. It was also observed that, although, there exist a unique endemic equilibria for the disease, this equilibria however is not stable. Numerical simulations of the model were carried out by implementing the MATLAB ODE45 algorithm for solving non-stiff ordinary differential equations. The results of these simulations are the effects of the various model parameters on each compartment of the developed model. Based on the findings of this research, necessary recommendations were made for the applications of the model to an endemic area.

Keywords: Mathematical Model, Stability Analyses, Lassa Fever, Equilibrium Points, Numerical Simulation.

DOI: 10.7176/MTM/9-6-04

Publication date: June 30^th 2019