A Class Of Dynamic Model Of The Propagation And Control Of Inlfuenza Virus

In the21st century,human’s ability is increasing,,the human can live moresafely and comfortably by changing the nature and can break the mystery of thecounless life through the scientific research.But we can’t ignore the infectionssymbiosised with human. When the global celebration of the50anniversary of theDNA double helix discovery, scientists announced they had completed thesequencing of the human genome, SARS virus, H1N1influenza virus continuouslyattack humans, become the most dangerous enemies of the human health. So theprevalence and prevention strategies of the epidemic is one of the problems inurgent need of solved．The dynamics of infectious diseases is an importanttheoretical method to research infectious diseases．This article puts forward a kindof dynamic model of influenza virus propagation and control,mainly researched onthe following content:First, the SIR model with index input and standard incidence ratio isestablished. The endemic equilibrium’s stability is analyze by using Lyapunovfunction, maximal invariant set principle and limit system theory.Second, the SIQR model with Quarantine measures is set up．Analyze thestability of the disease free equilibrium by using Lyapunov function, maximalinvariant set principle and limit system theory.using H criterion, Dulac functiondiscussed the stability of the endemic equilibrium, And the conclusion isnumerically simulated.Third, a SIR model with impulsive vaccination is established. By using thefrequency flash mapping we prove the existence of periodic solution, thedisease-free periodic solution of local stability is discussed with the help of theFloquet theorem, By using impulsive differential inequalities we get disease-freeperiodic solution global stability condition, we discuss the existence of positiveperiodic solutions with application of pulse bifurcation theorem. At last, the SIQR epidemic model with isolation and pulse vaccination is putforward．By using the frequency flash mapping proved the existence of periodicsolution． With the aid of the Floquet multiplier theorem, proved that thedisease-free periodic solution of local asymptotic stability, And given the thresholdvalueR0.Using pulse inequality we prove that periodic solutions are globallyasymptotic stability．When R0<1, Disease-free periodic solutions are globallyasymptotic stable, this means the disease in the population will be eliminated．Byusing impulsive differential equations bifurcation theorem obtained positiveperiodic solution bifurcation parameters. Finally, the model was numericallysimulated by using MATLAB7.1．...