Dynamic Behavior Of Stochastic Epidemic Model With Incubation

Recently,the spread of disease and the prevention and control is an important content of the world health organization's attention.Mathematical model has become the analysis and research on infectious diseases spread rule and one of the important tools of control strategy,recently by establishing deterministic model of infectious diseases to the research on the rules of the spread of infectious diseases have achieved fruitful results.In real life,the environment is a random variable,so the stochastic dynamics behavior of infectious disease model with machine has more practical significance.This dissertation will be white noise disturbance is introduced into the classic deterministic model of infectious diseases,respectively study random SEIR,SEIS and periodic stochastic SEIS infectious disease models to obtain some new results.The main contents are as follows:The first chapter mainly introduces the research background of infectious disease model,further with the incubation period of infectious disease model is illustrated by literature research,development and research achievements of predecessors,this article topic research work and prepare knowledge.The second chapter,considering the system subject to random fluctuations,random SEIR epidemic model is set up,in the presence of globally unique positive solution of the system,based on the application of Ito formula,Lyapunov function,the strong law of large Numbers of stochastic analysis theory to obtain the model has the sufficient conditions of ergodic stationary distribution;Disease is given the sufficient conditions of extinction.The third chapter,considering population mortality and disease transmission rate disturbance,random SEIS spread disease model with nonlinear incidence,in the presence of globally unique positive solution of the system,based on the application of Ito formula,Lyapunov function,the strong law of large Numbers of stochastic analysis theory,the study of random SEIS epidemic model in stationary distribution near the endemic equilibrium,if white noise intensity satisfies some conditions,the model has a stationary distribution,and the solution is traverse;In chapter 4,a periodic stochastic SEIS epidemic model was established by continuing to consider that the system was subject to random fluctuations.On the basis of the existence of a global unique positive solution of the system,Ito formula,Lyapunov function,law of powerful Numbers and other random analysis theories were applied to study the model The dynamic behavior of stochastic SEIS epidemic model with periodic coefficients and sufficient conditions for the existence of periodic solutions are given.The sufficient conditions for disease extinction are given.