An optimal control model for the transmission dynamics of Lassa fever

Abstract In this paper, a mathematical model for Lassa fever transmission dynamics with rodent logistic growth is developed and analysed. The stability analysis of the autonomous system of the model is presented. The sensitivity analysis of the parameters is performed using the Partial Rank Correlation Coefficient (PRCC) technique. The non-autonomous model is further analysed for stability of disease-free periodic equilibrium(DFPE) in terms of reproduction number ratio, $R_{0t}.$ It shown that DFPE is locally asymptotically stable when $R_{0t}1$. Additionally, the optimal control model is formulated with five control measures namely; personal protective equipment and avoiding hunting of rodents, proper handling of food, treatment and isolation, cleaning and disinfecting the environment, and rodent control. Simulations of the optimal control model show that the combined implementation of the five control measures reduce Lassa fever spread in the population. However, when there is limited resources to implement the five control measures, three or four combined control measures can be implemented provided that proper handle of food is among the combined control measures.