A Study Of Three Types Of Stochastic SIS Infectious Disease Models Driven By Mean Reversion Processes

Today,infectious diseases are a major problem for countries around the world.With the development of economic globalization,the very close interaction of people from all countries has accelerated the spread of diseases.Among the methods used in infectious disease research,the kinetic modelling of infectious diseases is an important method for studying infectious diseases.By building kinetic models,analyzing and numerically simulating the system,the development trend of infectious diseases can be predicted,and the development pattern of infectious diseases can also be understood.In this paper,the following three stochastic SIS infectious disease models are studied.Chapter 1 investigates the stochastic SIS infectious disease model with mean reversion for mortality.First,the existence and uniqueness of the global positive solution and the boundedness of the solution are demonstrated.In addition,the kinetic properties of the model are analyzed by obtaining thresholds for disease extinction and mean persistence,and the results show that the larger the fluctuation intensity?,the faster the disease extinction,while the smaller the fluctuation intensity?,the larger the number of infectious population.Finally,numerical simulations are performed.Chapter 2 investigates the SIS infectious disease model with mean reversion for exposure rates.First,the existence and uniqueness of the global positive solution and the boundedness of the solution are proved,then the stochastic fundamental regeneration number of the model is obtained,and it is also discussed that larger fluctuation intensities or lower regression rates can lead to the disease extinction,and finally,numerical simulations of the model are performed to illustrate the correctness of the results.Chapter 3 develops a stochastic SIS infectious disease model with isolation terms and mean reversion for exposure rates by building on existing SIS infectious disease models and considering the presence of isolator classes.First,the existence and uniqueness of the global positive solution and the boundedness of the solution are demonstrated.Moreover,thresholds for the persistence and extinction of the disease are obtained,and it is further shown that larger fluctuation intensities or lower regression rates can lead to extinction of the disease.Numerical simulations of the model are carried out according to the Milstein Higer Order Method.