The Mathematical Mechanism Of Malaria Transmission And Spatial-temporal Analysis Of Malaria Epidemic In China

Malaria is one of the most fatal vector-borne diseases in the world that are caused by the bites of infected female Anopheles mosquitoes or the transfusion of blood from a person carrying the Plasmodium parasites.The research on malaria control measures in this paper can provide theoretical guidance for malaria control work.This paper develops a compartmental model for malaria transmission with three control measures,including insecticide-treated mosquito nets,treatments and indoor residual spraying.The goal is to explore measures to control the spread of malaria.The paper derives the basic reproduction number,and analyzes the stability of disease-free equilibrium and the existence of endemic equilibrium.This work performs local sensitivity analysis and extended sensitivity analysis on parameters to evaluate the relative importance of parameters to the basic reproduction number.This paper applies Pontryagin's Maximum Principle to solve optimal control for mitigating malaria epidemic and find the necessary conditions for the optimal control.The goal is to keep costs as low as possible while reducing the number of infected humans.In this paper,Arc GIS 10.4 is used to describe the spatial-temporal evolution of the malaria epidemic in recent years in China,highlighting the areas with high incidence of malaria.It provides a reference for China to carry out targeted malaria elimination.Numerical simulations of the compartmental model indicate that the effective mitigation strategies lead to the greater reduction of both the mosquito population and infected human population.Thus,malaria can be eradicated by concurrently applying vector control via insecticide-treated mosquito nets and indoor residual spraying complemented with prompt treatment of infected people.By varying the parameters,this paper finds the reasonable values of the parameters.The simulation of the optimization model gives the effective combination of measures and the best implementation scheme when the weights are changed.The high incidence areas of malaria in China are visualized by the maps generated by GIS.