A Class Of Random Infectious Disease Model With Virus Mutation

Stochastic differential equations are not only applicable to many fields such as physics,finance,environment,electricity,control and chemistry,but also play an important role in biology,medicine and other fields.In real life,the spread of infectious diseases inevitably under the influence of random disturbance in the environment,so the stochastic model is used to describe the spread of infectious diseases can more accurately reflect its rule.Based on the deterministic model SIR and SIS of virus mutation,this paper USES Brownian motion as the noise form disturbance,and obtains the corresponding random model of SIR and SIS.For the SIR model of the virus mutation,this paper uses two different random disturbances,one is the random disturbance to the coefficient of infection rate,the other is the random disturbance to the whole model.Firstly,the global existence of the model solution is proved by using the proof method.Secondly,it is proved that the asymptotic behavior of the equilibrium of the disease-free equilibrium and the local disease equilibrium is proved.Finally,the numerical verification is carried out.For the SIS model of virus mutating,this model studies a class of diseases that are similar to AIDS or viral colds,and the infected patients were divided into the premutated patients and the patients with the mutation.Susceptible people were infected before mutation or after infection,and all of them became mutated patients before mutation,and after the mutation,the patient can only change from the former patient.First of all,we by constructing Lyapunov function,the global existence and uniqueness of the solution are obtained.Then we studied the model in the asymptotic behavior of the disease-free equilibrium and the endemic equilibrium,the results show that the parameters meet the requirements under the premise of equations in equilibrium asymptotically stable,and through the numerical simulation verifies the correctness of the conclusion.