Study On The Stability Of Epidemic Model Of Viruses Mutate

In this article, a few types of epidemic model of viruses mutate is studied.The disease-free equilibrium and endemic equilibrium of the stability, uniformpersistence are discussed. Main results are as follows:Firstly, a kind of SEIR epidemic model of viruses mutate with linearcontact rate is built. The basic reproduction number is obtained. The existenceconditions of the disease-free equilibrium and endemic equilibrium are given.By constructing Liapunov functional, the global asymptotically stability of thedisease-free equilibrium and endemic equilibrium are proved. The effectivenessof the theorem conditions is proved by numerical simulation. The recovery ratefor infected individuals with strain one is increased, the disease outbreak can becontrolled.Secondly, a kind of SEIR epidemic model of viruses mutate with nonlinearcontact rate is built. The basic reproduction number of the disease-freeequilibrium and endemic equilibrium are given. By constructing Liapunovfunctional, the global asymptotically stability of the disease-free equilibrium isgiven. By using the Hurwitz method, the locally stability of the endemicequilibrium is given. By using the comparison principle and qualitative theoryof the differential equations, the conditions of persistent is obtained. By usingnumerical simulation, the effective contact rate of individuals with strain one isdecreased, the prevalence of disease can be avoided.Lastly, the influence of viruses mutate time is considered, a kind of SIRepidemic model of viruses mutate with linear contact rate and delay is built. Theexistence conditions of the disease-free equilibrium, endemic equilibrium andsingle endemic equilibrium are given. By constructing Liapunov functional, theglobal asymptotically stability of the disease-free equilibrium is studied. Byusing the comparison principle and the theory of the delay differential equations,the conditions of persistent is obtained. By using numerical simulation, the feasibility of the conclusion and the global asymptotically stability of the singleendemic equilibrium are proved. The recovery rate for infected individuals withstrain one is increased, the prevalence of disease can be influenced.