Dynamics Analysis Of Stochastic SIQS Epidemic Models

Since ancient times,infectious diseases have been one of the factors hindering social development,so it is especially important to prevent and control infectious diseases.A large number of scholars have established corresponding mathematical models to analyze the spread of infectious diseases based on actual problems,and then optimize the control of infectious diseases Strategy.When an infectious disease breaks out,it takes a certain time to study its transmission route and develop a vaccine,so the development of efficient control measures is the first choice to prevent the spread of infectious diseases.One of the most direct means to prevent the spread and spread of infectious diseases and to control the source of infection is to isolate the infected people.At present,the research on the deterministic SIQS infectious disease model has achieved good results,and in actual life,The spread of disease is inevitably affected by environmental random factors.This academic paper considers three types of random SIQS epidemic models under the influence of environmental white noise,the main contents are as follows:The first part,considering the impact of media reports on infectious diseases,the fol-lowing deterministic SIQS epidemic model was established.The stability at the equilibrium point is discussed.The basic regeneration number of the system is given to₀.When₀?1,the disease-free equilibrium point is globally asymptotically stable.when₀>1,the local equilibrium point is globally asymptotically stable and the disease-free equilibrium point is unstable.Independent Brown motion is used to describe the random disturbance of the environment.We consider that the group contact rate is disturbed by white noise,the following stochastic SIQS epidemic model is established.By constructing suitable Lyapunov function and using It?o formula,strong number theorem,etc.We prove that the system has a globally unique positive solution,and obtain sufficient conditions for disease extinction and the large white noise can suppress the disease outbreak.Fokker-Planck equation and Markov semigroup theory are used to prove that the system is stable,The study shows that₀<₀,that is,random fluctuations in exposure affect the disease mechanical behavior,and increasing the influence of media coverage can reduce the number of people affected.Finally,the theory was proved by numerical simulation.Then,we are considering the random perturbation of population mortality,a stochastic SIQS epidemic model with saturated incidence under the influence of the media is established.By constructing suitable Lyapunov function,using the knowledge of related stochastic differ-ential equations such as It?o formula,the strong number theorem of martingale,the sufficient conditions for the extinction of the disease are discussed,and the solution of the system at the local equilibrium point is gradually.The Khasminskii method is used to obtain sufficient conditions for the system to have an ergodic stable distribution,Finally,we use numerical simulations to find that the number of infected people can be reduced through media reports.Finally,we study a stochastic SIQS epidemic model with Beddington-DeAngelis inci-dence with randomized environmental contact rate and mortality.Based on the existence of a globally unique positive solution,the It?o formula is used to construct a suitable Lyapunov function and the strong number theorem and under other conditions for the death of the disease.Constructing a suitable Lyapunov function,using It?o formula,strong number theo-rem and other tools gave sufficient conditions for disease extinction.We found that random perturbations in mortality and contact rate can suppress the spread of infectious diseases,and the theoretical results are finally verified by numerical simulation.