Dynamic Behavior Of Several Stochastic Infectious Disease Models

In recent years,due to the outbreak of the COVID-19 pandemic,the topic of infectious diseases is once again at the forefront.In order to fight the epidemic that endangers human life and health,human society takes a series of measures.More and more scholars are using mathematical models to describe the laws of the occurrence and development of infectious diseases,especially providing valuable public health intervention recommendations for disease control departments.Considering the influence of white noise disturbance on the dynamic behavior of epidemic models,this paper mainly explores the dynamic behavior of several types of stochastic epidemic models under white noise disturbance.The specific research contents are as follows:We study the dynamic behavior of a second-order stochastic perturbed SEIQV epidemic model with saturated incidence rate.Firstly,by establishing an appropriate Lyapunov function,the sufficient criteria for the existence and uniqueness of the ergodic stationary distribution of the model are derived.Secondly,the conditions for disease eradication in the epidemic model are established.Finally,the feasibility of our theoretical results is further verified by numerical simulations.We investigate the dynamic behavior of a second-order stochastic perturbed SIQRS epidemic model with temporary immunity.Firstly,by using Has’minskii theory and Lyapunov function method,we determine the stochastic critical valueR₀^S related to the basic reproduction numberR₀.It is proved that there is a unique ergodic stationary distribution whenR₀^S（29）1.In addition,we obtaine sufficient conditions for the extinction of the diseaseR₀^I（27）1.Finally,the conclusions are demonstrated by computer simulation.We discuss the dynamic behavior of a SEIR epidemic model with n-order stochastic perturbations.Taking into account the complexity of environmental fluctuations in the real world,we design and explore a SEIR epidemic model with n-order stochastic perturbations.By using an inequality and the method of constructing Lyapunov function,we prove that the stochastic model has a unique ergodic stationary distribution and obtain the sufficient conditions for disease extinction under the stochastic model.In this paper,considering that stochastic perturbations will depend on the high-order terms of each population,we mainly use the theory of stochastic differential equations to study the dynamic behaviors of three types of infectious disease models under white noise interference.Compared with linear white noise interference,the application of nonlinear white noise stochastic perturbations to describe the actual situation is more in line with the law of transmission of infectious diseases,and it also provides theoretical support for the development of reasonable and efficient control strategies.