A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis

Abstract

A co-infection model for onchocerciasis and Lassa fever (OLF) with periodic variational vectors and optimal control is studied and analyzed to assess the impact of controls against incidence infections. The model is qualitatively examined in order to evaluate its asymptotic behavior in relation to the equilibria. Employing a Lyapunov function, we demonstrated that the disease-free equilibrium (DFE) is globally asymptotically stable; that is, the related basic reproduction number is less than unity. When it is bigger than one, we use a suitable nonlinear Lyapunov function to demonstrate the existence of a globally asymptotically stable endemic equilibrium (EE). Furthermore, the necessary conditions for the presence of optimum control and the optimality system for the co-infection model are established using Pontryagin’s maximum principle. The model is quantitatively analyzed by studying how sensitive the basic reproduction number is to the model parameters and the model simulation using Runge–Kutta technique of order 4 is also presented to study the effects of the treatments. We deduced from the quantitative analysis that, if there is an effective treatment and diagnosis of those exposed to and infected with the disease, the spread of the viral disease can be effectively managed. The results presented in this work will be useful for the proper mitigation of the disease.

Keywords

• onchocerciasis
• Lassa fever
• co-infection
• global stability
• optimal control
• periodic variational vectors