Optimal Control Analysis of a Mathematical Model for Recurrent Malaria Dynamics

Recurrence of malaria symptoms after treatment constitutes one of the major factors affecting malaria control in the population. The transmission of malaria will persist in the population, if effective and considerable control measures are not put in place. In this study, a time-dependent deterministic mathematical model focusing on the role of preventing and controlling the transmission dynamics of recurrent malaria is considered and analyzed. The formulated non-autonomous model is justified by exploring the sensitivities of the basic reproduction number to changes in the parameters of its time-invariant version. By using optimal control theory, the existence of four optimal control functions, including personal preventive effort against mosquito bites, anti-relapse measure, anti-malaria treatment and insecticide spraying, is qualitatively established and the control quadruple is characterized using Pontryagin’s maximum principle. Numerical simulations of the optimal control problem are conducted to show the effects of doubling optimal control functions on the recurrent malaria system through graphical demonstrations.