Dynamical Analysis Of COVID-19 Model With Secondary Vaccination Induced By Noise

Novel coronavirus pneumonia(COVID-19)is an infectious disease caused by severe acute respiratory syndrome coronavirus.It can cause serious sequelae or death due to dyspnea,headache,loss of taste or smell,seriously affect the development of society and people’s lives around the world.Since the outbreak of COVID-19,people has begun to take various measures to prevent and control the development of the epidemic,including isolation,vaccination,etc.Therefore,from the perspective of biological mathematics,based on the dynamics of infectious diseases and other related theories,it has important theoretical and practical significance for the prevention and control of COVID-19 which using mathematical models to study the transmission laws and epidemic trends of COVID-19 epidemic with secondary vaccination.Therefore,this paper mainly considers the impact of environmental noise and secondary vaccination in the process of disease transmission,then studies the dynamical behavior of infectious disease models induced by different environmental noise.The specific work is as follows.1.The dynamical behavior of a stochastic COVID-19 model with secondary vaccination under the influence of white noise is studied.Firstly,a stochastic COVID-19 model is established based on white noise,secondary vaccination and bilinear incidence rate.Secondly,the existence and uniqueness of global positive solutions are proved by stochastic Lyapunov function theory for the model,then sufficient conditions for the extinction of diseases are obtained.Finally,the theoretical results is verified by numerical simulation.The results show that secondary vaccination can effectively control the spread of COVID-19 epidemic and the intensity of random intervention can promote the extinction of infected people.2.The dynamical behavior of COVID-19 model under the influence of Lévy noise is discussed.Firstly,a stochastic epidemic model driven by white noise and Lévy noise is established based on the secondary vaccination.Secondly,the existence and uniqueness of global positive solutions of the stochastic model are proved using stochastic differential equations and Lyapunov function theory,then the asymptotic behavior at the disease-free equilibrium point is studied.Thirdly,the sufficient conditions for the extinction of infectious diseases are proved.Finally,the theoretical results is verified by numerical simulation.The results shows that different noise intensities can affect the extinction of diseases.