Dynamic Analysis Of Several Virus Infection Models

Infectious diseases threat human health,most of infectious diseases are implemented byvirus infection.Using the medical test data of the virus,and using methods of mathematicalmodel study of the dynamic behavior of infectious virus infection,it is signifcant to medicalinspection,control,treatment and research of infectious disease virus infection.In this paper,according to the characteristics of the virus infection,by using the methodof mathematical model,mainly studied the following two questions:The frst problem research a class of immune regulation of viral infection model withtime delay.About the virus infection model considering the infuences of one or two factors,such as the model with nonlinear incidence of virus infection,the model with time delay ofvirus infection,etc.,domestic and foreign scholars have been studied.In the actual transmis-sion of the virus,at the same time,it is often a variety of factors afect the virus infection,andit is of important signifcance to control the spread of the virus.Based on the above rea-sons,saturated incidence and the immune regulation of viral infection model with time-delayis set up,we prove that if R0≤1,τ is arbitrary value,then the disease-free equilibrium islocally asymptotically stable,when R0>1,we prove that there exists a unique endemic equi-librium,and under certain conditions,there is a τ0>0,when τ <τ0,the endemic equilibriumis locally asymptotically stable;while τ> τ0,it is unstable.In the end,numerical simulationsare carried out to explain the mathematical conclusions.The second problem is investigated for a class of general form CTL immune model ofvirus infection.It has been researched about linear and bilinear,saturation of CTL immunereaction of the virus infection models.By studying these results,fnding that there are a lotof common problem,when that incidence in abstract function is given can also get someresults,then a virus infection model with general form CTL immune is set up,it presents thecorresponding threshold,through the analysis of the form of R0,with the increase of immuneregulation,the value of R0will be smaller.By constructing Lyapunov function,we prove thatif R0<1,then the disease-free equilibrium is globally asymptotically stable,when R0>1,we prove that there exists a unique endemic equilibrium,using Routh-Hurwitz criterion,and itis locally asymptotically stable.The research not only involved the related theory of biological dynamic system,but alsoinvolved algorithm theory in the numerical simulation analysis,and completed the relatedsimulation and calculation with applying mathematic software.