Global Stability Of Epidemic Model With Distributed Delay And Relapse

In this thesis,we mainly study the difference of time delay and relapse of epidemic.The epidemic model with distributed delay and relapse in homogenous and heterogeneous population environment is established.We also study the global dynamics of model and biological meaning.The main work of this paper as follows.Based on theory of Chapter 1 and Chapter 2,In Chapter 3,we establish and study the epidemic model with distributed delay and relapse in homogeneous pop-ulation.We calculate the basic reproduction number R₀ of the system,and show that the global dynamics is completely determined by the basic reproduction num-ber.By constructing Lyapunov functionals and applying the LaSalle invariance principle,we draw the conclusion:if R₀<1 the infection-free equilibrium is global asymptotic stability;R₀>1 the endemic equilibrium is global asymptotic stabil-ity.Finally,the sensitivity of the parameters about R₀ is analyzed.We present a strategy for disease prevention and control.In Chapter 4,we establish and study the multi-group epidemic model with distributed delay and relapse in heterogeneous population.The basic reproduc-tion number R₀ of the system is obtained by calculating the spectral radius of the reproduction matrix,we show that the global dynamics of system is completely determined by the basic reproduction number,by constructing the Lyapunov func-tionals then applying the LaSalle invariance principle and Matrix tree theory,we draw the conclusion:if R₀<1 the infection-free equilibrium is global asymptotic stability,and the disease is eliminated in the subgroups;Ro>1 the equilibrium of endemic disease is global asymptotic stability,and the disease will develop into endemic in each subgroup.Finally,we present the strategy for disease prevention and control.In Chapter 5,we establish model based on chapter 4,which considers the ef-fect of random perturbatiot.We show that the system is stochastically asymptoti-cally stable,if the intensity of random perturbation ?_kj satisfies certain condition.