A mathematical modeling and optimal control analysis of the effect of treatment-seeking behaviors on the spread of malaria

Malaria, an infectious disease transmitted by mosquitoes and caused by the Plasmodium parasite, poses a significant global public health challenge, especially in areas lacking modern medical infrastructure. Traditional medicine often serves as either a primary or complementary treatment avenue. This study introduces a novel deterministic model that considers the impact of treatment seeking-behaviors on malaria transmission dynamics. Expanding upon the existing model, we incorporate distinct groups: individuals seeking treatment at health facilities and those self-treating with traditional remedies, which lack clinical validation. The study employs mathematical techniques for a comprehensive analysis of the model, including positivity, boundedness, existence and uniqueness, equilibrium, reproduction number, sensitivity, optimal control, and numerical simulations performed using MATLAB and the fourth-order Runge-Kutta method. Furthermore, we explore three time-dependent optimal control variables: antimalarial drug treatment, personal protective measures like ITNs, and promoting awareness to discourage inappropriate traditional medicine usage, all aimed at reducing disease transmission. Sensitivity analysis helps identify key parameters affecting malaria dynamics. Notably, increased utilization of health facilities for treatment significantly reduces the basic reproduction number, highlighting the importance of effective healthcare interventions. Numerical simulations underscore the vital role of treating infected individuals at health facilities in malaria eradication efforts. Optimal control analysis suggests that a combination of the three control strategies is most effective in combating malaria. This provides insights for public health policies to address the risk factors of using clinically not validated traditional medicine in malaria-endemic areas.