A Mathematical Model and Sensitivity Analysis of Lassa Fever with Relapse and Reinfection Rate

Abstract

In this research paper, we depict an unprecedented four-dimensional ordinary differential equation modeling the dynamic transmission of the Lassa fever virus incorporating relapse and reinfection rate. Recent studies showed that the recovered individuals from Lassa fever can again be susceptible; which contradicted the common assumptions made by different researchers on modeling of Lassa fever. So, this article corrects and states the implications of the assumptions on the population density. The numerical simulations unveil the effect of relapse, reinfection, and treatment rate in the affected population. Performing sensitivity analysis suggests all new incorporated parameters can impact the infection dynamics substantially. The stability analysis was carefully estimated where expression for each compartmentalized variable was calculated at both disease-free and persistence (endemic) equilibrium. Also, the basic reproduction number of the novel model was calculated using the Next Generation Matrix. The analytical results justify that the persistence (endemic) and the disease-free equilibrium are locally and globally asymptotically stable using both Routh Hurwitz Criterion and Comparison Theorem.

Keywords: Lassa fever, Reinfection rate, Relapse rate, Treatment rate, Sensitivity analysis.