Optimal Control Analysis of Malaria Transmission in the Presence of Insecticide Resistance and Climate Variability in Kenya

Malaria remains a major public health concern in Kenya, where changing climatic conditions, insecticide resistance, and mosquito behavioral adaptations continue to challenge control efforts. This study develops and analyzes a climate-sensitive malaria transmission model that incorporates mosquito behavior, insecticide resistance, and vector–human ecological dynamics to identify optimal control strategies for the Kenyan context. The model’s well-posedness was established, the basic reproduction number R0 computed using the next-generation matrix method, and the stability of equilibrium points assessed. Spatial analysis of R0 was performed using temperature and rainfall raster data to map transmission risk across Kenya under varying insecticide use scenarios. Results indicate that regions with climatic conditions favorable for vector survival, particularly parts of the Eastern and Western regions, experience higher transmission intensity. Simulations show that while insecticide use (deltamethrin or permethrin) substantially reduces malaria prevalence, resistance δv=0 results in R0>1 and sustained transmission. An optimal control problem incorporating personal protection, antimalarial treatment, and vaccination was formulated and solved using Pontryagin’s Maximum Principle. The most effective reduction in malaria prevalence was achieved when all three interventions were applied simultaneously, with infections declining to zero within 10 days. These findings highlight the importance of integrating vector behavior, climate variability, and resistance dynamics into malaria models and support the use of combined intervention strategies to enhance control efforts in Kenya.