| In recent years,all kinds of infectious diseases have been endangering human health and life,so it is of great significance to study the spreading law of infectious diseases for the prevention and control of infectious diseases.Meanwhile,The research on dynamical behaviors of biological mathematics with stochastic perturbation model has been widespread attention to domestic and international scholars.Therefore,utilizing stochastic mathematical models to analyze the dynamical behaviors of species can reflect the reality more accurately.In this paper,we mainly study the dynamic behavior of two types of rabies models with stochastic perturbation.The main contents are summarized as follows:1.Ergodicity and extinction of a rabies model with dog-to-human transmission under regime switching.When system is disturbed by both white and telegraph noises,firstly,we prove the existence of the unique global positive solution.Secondly,by using the theory of Markov regime switching,we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model.Finally,we establish sufficient conditions for the extinction of diseases.2.Positive recurrence and extinction of a rabies model with dog-CFB-human transmission under regime switching.When the system is disturbed by telegraph noise,firstly,we prove the existence of the unique global positive solution of the system.Then we establish sufficient conditions for the extinction of stochastic rabies model.Finally,by constructing the appropriate Lyapunov function,we prove the existence of positive recurrence of the solution to the model. |
