On the stability analysis of a mathematical model of Lassa fever disease dynamics

Abstract

Lassa fever is a deadly disease transmitted through ingestion of food that is contaminated with infected rodent’s saliva, urine or excreta, infected person and inhalation of the aerosol. In this paper, we investigated the stability analysis of the transmission dynamics of Lassa fever mathematical model. The disease-free equilibrium was shown to be both locally asymptotically stable and globally asymptotically stable, the later being shown using comparison theorem. The basic reproduction number, which is an important parameter in the control of Lassa fever infection, was calculated using the next generation method. We have also shown that the endemic equilibrium point, exists for and has been noted that this endemic equilibrium is unique and globally asymptotically stable based on Lyapunov Function. This result implies that Lassa fever disease can be totally eradicated when the basic reproduction number is less than unity. We therefore advocate for health policies that will keep the basic reproduction number below one, thereby keeping the occurrence of Lassa fever under control.