Model And Study Of Delay Infectious Diseases With Vaccination And Media Effects

With the globalization trend,new and recurring infectious diseases are threatening people's health and life,such as H1N1,avian influenza H7N9,HIV / AIDS,and now,the outbreak of the Coronavirus Disease-19(COVID-19),currently there are no good treatments,which affects human survival and development seriously.In the new media era,the public health department can apply the internet,wireless communication networks,satellites and other channels,as well as terminals such as computers,mobile phones,and digital televisions,to promptly and efficiently issue early warnings of epidemic conditions and publicize disease prevention measures to the public,that can strengthen the people's awareness of prevention and control.Wuhan has adopted "closed city" isolation after the outbreak of the COVID-19,which effectively controlled the spread of the disease.In addition,vaccination is an effective means to prevent certain infectious diseases,but vaccination will take some time to produce immunity,and so there exists an immune delay.The data reported by the media comes from previous statistics,so it has a time delay,and the time delay may change the dynamic characteristics of the original dynamic system and cause branching phenomenon.Therefore,the effect of time delay should be considered when modeling,which will be more realistic.We establish three types of epidemic models to explore the effect of media delay and immune delay,as well as the dynamic characteristics of COVID-19.First,in order to study the effect of media delay on the spread of infectious diseases,we constitute a class of infectious disease model with time delay in the second chapter,the calculation formula of the basic reproduction number is given,the stability of the equilibrium is analyzed,and the existence of Hopf bifurcation is also proved.Numerical simulations according with measles is provided at last.The results indicate that both media delay and the possibility of infection in some consciously susceptible populations can increase the number of infected and postpone the peak time.Second,considering that individuals who have been vaccinated against influenza have a certain immunization period,an SEIAR influenza model with immune delay is established in the third chapter to explore the impact of the following three comprehensive interventions,"media,vaccination and antiviral treatment" on influenza transmission.By constructing the Lyapunov function and combining with the RouthHurwitz criterion,the stability of the disease-free equilibrium and the endemic equilibrium is analyzed,and a sufficient condition for the existence of Hopf bifurcation near the endemic equilibrium is obtained when the immune delay is non-zero.Numerical simulations show that comprehensive consideration of the three types of interventions is the most effective.Finally,based on the transmission mechanism of the Coronavirus Disease-19(COVID-19),we develop an SEICAR epidemic model,in which both asymptomatic infectious patients and latent patients are infectious.Through sensitivity analyses of each parameter of the control reproduction number and the endemic equilibrium,three effective control strategies are proposed.The results indicate that the control reproduction number can be more accurately evaluated when we consider the infectivity of the latently infected and asymptomatic patients.Furthermore,this will provide a more scientific reference for making prevention and control policies.