Modeling the effect of Wolbachia to control malaria transmission

Abstract

Female Anopheles mosquitoes are the primary vectors responsible for malaria transmission. The control of malaria is essential for humankind. In this study, we introduce a nonlinear deterministic model to control malaria disease by deploying Wolbachia bacteria into the Anopheles mosquitoes. Further, we study the effect of Wolbachia on temperature variation in tropical and subtropical regions of the world. We analyze the model for its positivity and boundedness with an initial condition in a specific set so that the model is well-defined mathematically and meaningful epidemiologically. We find the malaria-free equilibrium points of the model and analyze the local stability of all the equilibrium points. We calculate the basic reproduction number by the next-generation matrix method, which shows the stability of malaria-free equilibrium. Then we explore malaria present endemic equilibrium in both cases: Wolbachia-infected and Wolbachia-free possibilities. We observe that the number of infections is less in the Wolbachia-infected equilibrium case, and we find that Wolbachia can reduce malaria transmission in all temperature conditions. The sensitivity analysis of all different parameters is also calculated. We demonstrate the optimum temperature (from 22 °C to 28 °C) by numerical simulation where the malaria exposure and transmission rate is high. We can apply the work in all subtropical and tropical regions to control malaria transmission worldwide.