Dynamic Analysis Of Three Types Of Infectious Disease Models Incorporating Some Control Measures

Infectious diseases,which can infect the susceptible by pathogens,may spread from person to person,animal to animal,or human to animal.Nowadays,there are more and more kinds of infectious diseases.All kinds of infectious diseases have brought serious harm to human health.The global public health system implements a variety of measures to prevent and control epidemic diseases,such as providing timely and effective treatment,isolating infected people to reduce transmission,and vaccinating the susceptible to build herd immunity,and so on.Usually,researchers study infectious diseases by constructing mathematical models,because this not only can describe the mechanism of disease transmission,but also can predict the development trend of disease based on the numerical simulations,therefore it can help to propose theory foundation for prevention and control.According to the transmission mechanism of three kinds of infections,the corresponding mathematical models are established to discuss the dynamics of those disease transmission.The main research contents are as follows:First,in order to study the influence of the isolation and exposed period of patients on mumps,we establish a class of SEIAQR mumps model,and then calculate the control reproduction number of the model,according to the Hurwitz criterion,it is proved that the disease-free equilibrium(DFE)of the system is locally asymptotically stable.Through constructing the Lyapunov function and making use of Lyapunov-La Salle theorem,we prove that DFE is global asymptotic stable,which means that mumps will perish and disappear finally.It is verified that there is only one endemic equilibrium,and the endemic equilibrium is globally asymptotically stable,which indicates that mumps will always exist and become endemic.Second,in order to study the treatment and prevention of the spread of hepatitis C,an SCITR model is developed according to the transmission mechanism of hepatitis C.The control reproduction number is given,and then by constructing appropriate Lyapunov function and the Lyapunov-La Salle theorem,the global stability of the two equilibria are testified.Finally,the sensitivity analysis and numerical simulations are carried out.The results show that it can effectively reduce the scale of the outbreak of hepatitis C by enhancing the awareness of people and improving the treatment of the disease.Third,we construct a class of SEAICR model of COVID-19 in order to investigate the transmission effect of the COVID-19 about the transition from partially asymptomatic infection to symptomatic infection.We obtain the control reproduction number,and testify the local stability of the disease-free equilibrium of the model.Subsequently,the sensitivity of the control reproduction number is given.The results of the numerical simulations show that the transmission of COVID-19 can be controlled better by increasing the proportion of the latent infection,or reducing the conversion rate of the asymptomatic infection to symptomatic infection,which means that the asymptomatic infection should be detected as soon as possible and given treatment more timely.