Dynamics Of Several Types Of Stochastic Epidemic Models With Periodic Parameters And Markov Switching

To study the influence of environmental disturbance on epidemic models,three types of stochastic epidemic models with periodic parameters and Markov switching are proposed.The threshold of extinction and persistence in the mean and other properties are investigated via using the theory of stochastic differential equations and Hasminskii theory.The first chapter introduced the research background,status and meaning of the epidemic model,briefly described some preliminaries knowledge about stochastic differential equations and gave the main work of the full text and innovation points.The second chapter studied a stochastic SIS epidemic model with double epidemic hypothesis with periodic parameters.Firstly,the existence and uniqueness of the global positive solution are proved.Secondly,the conditions for the extinction of disease and the existence of nontrivial T periodic solutions are established.Finally,the theoretical results are verified by Matlab numerical simulation.Its biological significance indicates that the high-intensity white noise can lead to the extinction of periodic diseases.The third chapter presented a class of stochastic SIQS epidemic model with periodic parameters.Firstly,the existence and uniqueness of the global positive solution are verified.Secondly,the thresholds for extinction and persistence in the mean and the sufficient conditions for the existence of non-trivial T periodic solutions are obtained.Finally,the corresponding theoretical results are verified by Matlab numerical simulation.Its biological significance shows that the high-intensity white noise can lead to the extinction of periodic diseases.The fourth chapter investigated a class of stochastic SIQS epidemic model with Markov switching.Firstly,the existence and uniqueness of the global positive solution are demonstrated.Secondly,the thresholds for extinction and persistence in the mean and the sufficient conditions for the existence and uniqueness of the ergodic stationary distribution are obtained.Finally,the corresponding theoretical results are verified by Matlab numerical simulation.Its biological significance indicates that the high-intensity environmental disturbances are conducive to controlling the outbreak of disease.The fifth chapter summarized the main contents of the full-text research,explained the biological significance of the corresponding conclusions and looked forward to the future work.