Mathematical analysis of a Lassa fever model in Nigeria: optimal control and cost-efficacy

In this study, we extend an existing Lassa fever model by incorporating four time-dependent control functions which are identified as a preventive strategy, treatment care, and rodent reduction. The six compartmental nonlinear optimal control problem is developed and analyzed. We employed Pontryagin's maximum principle for the analytical characterization of the optimality system, and we established control measures suitable for reducing the spread of Lassa fever in the community. Numerical simulations of the optimality system were performed on Matlab using the fourth-order Runge-Kutta forward-backward sweep method, to demonstrate the theoretical findings. We further carried out a comprehensive cost-effective analysis to investigate the strategy that is most cost-effective among all the eleven combinations of control implementation. The results reveal that the single preventive strategy targeted at preventing the transmission of the Lassa virus from infectious rodents to humans is considered the most cost-effective strategy among others in this study. Overall, this research sheds light on the cost of each combination of control strategies, informing the public about the strategy to implement based on the population's financial resources.