Modelling And Analyzing Two Classes Of Biodynamical Models

Dengue and schistosomiasis are diseases in which infected mosquitoes and infected snails are transmitted between humans or animals,respectively.This disease transmitted through the media is a serious threat to people's health and has been classified by the World Health Organization as a type of infectious disease that needs to be protected.Based on some typical characteristics of vector diseases such as dengue fever and schistosomiasis,two classes of biodynamical models are established and analyzed:One is based on the growth and development characteristics of mosquitoes.The time-delay is used to describe the maturity stage of mosquitoes.The mosquito population control model with time-delay and different delivery methods was established and studied.The model analyzes the effects of sterile mosquitoes three delivery methods(constant delivery,proportional delivery,saturated delivery)on the dynamics of wild mosquito populations.Particularly,when the three delivery methods were analyzed,interesting dynamic phenomena were obtained,such as the Hopf bifurcation.Finally,the theoretical results were verified by numerical simulation,an effective strategy for controlling the population of wild mosquitoes is given.The other is the establishment and study of a model of schistosomiasis with agricultural pollution.The properties presented in the model are discussed,for example,the Hurwitz criterion is used to prove the local asymptotic stability of the trivial equilibrium point and the disease-free equilibrium point,global asymptotic stability of the trivial equilibrium point and the disease-free equilibrium point is proved by constructing the Lyapunov function.In addition,the uniform persistence of the system is studied,and the theoretical results obtained are verified by numerical simulation,the sensitivity of the parameters in the system is analyzed,the effective measures to control the outbreak of schistosomiasis are given.