Mathematical modelling and optimization analysis of Malaria infection in the presence of insecticide resistance and climate variations in Kenya

Abstract

Over the years, control efforts to curb malaria transmission have been initiated and implemented by World Health Organization (WHO). These control efforts however rely on the use of insecticide-based control interventions which has enhanced the emergence and persistence of insecticide resistance to almost every insecticide class used. This study determines the optimal combination strategies for malaria control in the presence of insecticide resistance and climatic variation in Kenya. A deterministic model representing malaria transmission dynamics in the human and mosquito population is formulated and studied. The model equations are solved numerically using fourth and fifth order Runge-Kutta methods while the optimal control framework is solved numerically using forward-backward sweep method. The basic reproduction number R0 is derived and the disease-free equilibrium is shown to be locally and globally asymptotically stable. Sensitivity analysis reveals that the resting rate of susceptible mosquitoes αs and the mosquito mortality rate due to the use of insecticides δv are the most influential parameters in determining malaria transmission dynamics. Numerical simulation results show that in the presence of insecticide resistance, R0 is 1.2721 implying that malaria disease persists in the population. The spatial distribution of the reproduction number across Kenya further show that regions whose climatic conditions are favourable for malaria vector survival experience higher malaria transmission compared to areas whose climatic conditions are less favourable for vector survival and development. Additionally, based on optimal control analysis, the best malaria control intervention is when personal protection, treatment and vaccination are used simultaneously. This study reveals that insecticide resistance and climatic variation have a significant impact in the spread of malaria. Therefore, the study’s findings can be adopted by national malaria control program stakeholders in the fight against malaria in Kenya.