The Study Of Stability Of Stochastic Model Of Malaria Affected By The External Environment

The spread of some diseases relies on the media, such as malaria depending on anopheles, and the temperature of the surrounding environment and cleaning conditions determine whether the media can live sustainably. The temperature of the surrounding environment and sanitation are random, so that the outbreak of the diseases and extinction also has randomness. From a deterministic groups-anopheles model, the paper analyzes the stability of the deterministic model. Considering the randomness of temperature variation and environmental sanitation, it uses a stochastic model with a markov jump to construct a Gaussian diffusion model, and analyzes the probability and the mean of the first passage time to hit boundary.This paper is organised as:The first chapter introduces the background and significance of research topic, the current research status of malaria at home and abroad. The second chapter is an overview of prepare knowledge. The third chapter builds a SIS model of malaria with random disturbance from deterministic malaria model, then studies the stability of the disease-free equilibrium and the endemic equilibrium. Then analyzes the random malaria model probability and the mean of the first passage time to attract boundary. Finally, numerical simulation can verify the correctness of conclusion of the deterministic model.