Establishment And Dynamic Analysis Of Three Types Of Biological Mathematical Models

This article has established and discussed three types of biological mathematical models.The first type is about the stability analysis of the drug epidemic model,and the second type is about the persistence and extinction analysis of the vaccination infectious disease model under the disturbance of white noise.The third category is to discuss the existence of periodic solutions of the Leslie-Gower predator-prey model with Holling-III type prey self-predation:First,based on the recurrence rate of drug use,a drug epidemic model was established,and the population was divided into four categories at time t:susceptible people,drug addicts,temporary and permanent addicts,mainly use the theory of differential equations to obtain the basic reproduction number of the model R₀ and perform sensitivity analysis.We prove that if R₀<(?₁A)/(?(?+?₁))<1,the disease-free equilibrium point is globally asymptotically stable,if R₀>1,it proves the system exists the equilibrium point,and the existence conditions of its local asymptotic stability are discussed.At the same time,it is analyzed that the proposed model may have forward and backward branching conditions.In addition,three different parameter control strategies are proposed for the model and numerical simulation is carried out,and finally the best control strategy for this drug epidemic model was obtained.Second,the dynamic behavior of a type of vaccination infectious disease model under the disturbance of white noise is discussed.This system has a unique global positive solution under the initial value condition,and then,it gives the threshold for controlling the emergence and death of infectious diseases,and by constructing the V function,using the Ito formula,it is proved that when R₀^s<1,the disease will be extinct;when (?)>1,the disease will last.Finally,the existence of the periodic solution of the Leslie-Gower time-delay predator-prey model with Holling-? prey self-eating is studied,and obtains the sufficient conditions for the existence of the periodic solution.