Modeling and Optimal Control Analysis of Lassa Fever with Lockdown and Treatment Interventions

Abstract

Lassa fever is an acute zoonotic viral disease caused by the Lassa virus and remains a major public health concern in endemic regions. In this study, a mathematical model is proposed to investigate the transmission dynamics of Lassa fever incorporating hospital quarantine and control interventions in the form of lockdown measures and treatment strategies. The model considers both human to human and rodent to human transmission pathways. The model admits two equilibrium points, namely the disease free equilibrium and the endemic equilibrium. The existence and local stability of these equilibria depend on the basic reproduction number, $R_0$. The disease free equilibrium is locally asymptotically stable when $R_0<1$, whereas the endemic equilibrium exists and becomes locally asymptotically stable when $R_0>1$. Sensitivity analysis is performed to identify the parameters that most strongly influence disease transmission. The results indicate that the human to human transmission rate, the recovery rate of infectious individuals, and the treatment uptake rate are among the most influential factors affecting disease spread. An optimal control problem is formulated and analyzed using the Pontryagin Maximum Principle to determine effective intervention strategies that minimize both the infected population and implementation costs. Numerical simulations demonstrate that treatment interventions significantly reduce the number of infected individuals, while the combined implementation of lockdown and treatment controls provides additional benefits in reducing disease transmission. These findings provide qualitative insight into the role of quarantine and intervention strategies in controlling Lassa fever transmission.