Investigating the Role of Antimalarial Treatment and Mosquito Nets in Malaria Transmission and Control through Mathematical Modeling

Malaria is a significant global health challenge. This devastating disease continues to affect millions, especially in tropical regions. It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes. This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria, incorporating both human and mosquito populations. We aim to identify the key factors driving the endemic spread of malaria, determine feasible solutions, and provide insights that lead to the development of effective prevention and management strategies. We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points. Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one, whereas an endemic equilibrium persists when this threshold is exceeded. Sensitivity analysis identifies the most influential mosquito-related parameters, particularly the bite rate and mosquito mortality, in controlling the spread of malaria. Furthermore, we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments, use of larvicides, and the use of insecticide-treated mosquito nets for optimal control analysis. The results show that optimal use of mosquito nets, use of larvicides for mosquito population control, and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs. The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.