Mathematical Modeling And Dynamic Analyzing Of Multi-homing Echinococcosis Transmit

Infectious disease dynamics uses parameters and variables to express the spread of different infectious diseases,influencing factors,etc.with differential equations,establish a compartment model,and use related theories of differential equations to study whether the infectious disease will die in a few years,or Becoming an endemic disease in the area,as well as the conditions for the disappearance of infectious diseases,Infectious disease dynamics are important theoretical basis for preventing and controlling infectious diseases.Based on the basic theory of infectious disease dynamics and differential equations,this paper studies the legal C-type infectious diseases:echinococcosis,in China,predicts the future epidemic trend of echinococcosis,and formulates prevention and control strategies for echinococcosis.Echinococcosis is a zoonotic parasitic disease caused by Echinococcus.In many prov-inces and cities of China is harmed by echinococcosis,which seriously affects the safety of people's lives and property.It is urgent to formulate appropriate prevention and measures to control the spread of echinococcosis.In order to study the extinction conditions of echinoc-occosis,this paper uses infectious diseases dynamics to study echinococcosis.The research includes two parts:one is the modeling and stability analysis of the transmission dynamics of the standard incidence of echinococcosis;the other is the existence and global attraction of the periodic solution of the transmission dynamics model with seasonal influence.First,this paper introduce the transmission process of Echinococcosis,and current sta-tus of research on Echinococcosis by using infectious diseases dynamics.Second,this paper introduce some definitions,theorems of ODE and infectious diseas-es dynamics.Third,establish a class of Echinococcosis dynamics model with standard incidence.U-sing the Lyapunov function method proved that when the basic reproductive number R₀<1,disease-free equilibrium globally asymptotically stable,and when the basic reproductive n-umber R₀>1 and??+c?I1*??1S1*,the endemic equilibrium global asymptotic stability.Se-nsitivity analysis of models using data from the literature,the results show that the transmi-ssion rate from dog to livestock have great influence on the transmission of Echinococcosis.Finally,evaluate the control strategy,the results show that complex control is most econo-mical and feasible.Fourth,in order to consider the influence of seasonality on Echinococcosis,establish a class of Echinococcosis dynamics model,whose infection rate and the mortality rate of wo-rm's egg in the environment is vary with season.First,the paper give the basic reproductive number.By analysis show that the control of disease is depend on the basic reproductive n-umber R₀.The disease-free equilibrium is globally asymptotically stable when R₀<1,and when R₀>1,disease-free equilibrium is unstable,and the system is uniformly persistent,e-xists a positive periodic solution and it is globally attractively.Simulation checked the con-sistency between reality and theory use matlab.At last,the paper makes a summary and propose the prospect.