Complex Dynamics Of Tuberculosis Model With Media Coverage

Tuberculosis?TB?is a common and fatal infectious disease.It has become a chronic infectious disease that threatens human health worldwide.Thus,many scholars have carried out a lot of excellent research on the transmission mechanism and prevention strategy of TB.In the new media era,media coverage is the source of much important public health information.Therefore,we construct TB models with media coverage,study their stability,bifurcation and optimal control,and give numerical simulation to verify and popularize the theoretical results.In Chapter 1,we introduce the research background and current situation of TB,and give the preparatory knowledge related to this paper.In Chapter 2,we study a TB model with fast and slow progression and media coverage.By means of the next-generation matrix,we obtain the basic reproductive number R₀.When R₀<1,the local asymptotic stability of the disease-free equilibrium P₀is obtained by the Hurwitz criterion.By constructing the appropriate Lyapunov function,we prove the global asymptotic stability of the disease-free equilibrium P₀.In addition,when R₀>1,we discuss the existence and the local stability of each endemic equilibrium.By using the center mani-fold theorem,we get a forward and backward bifurcation.Furthermore,we give a numerical result about a Hopf bifurcation occuring when?passes through its critical value?^*.At last,we also use numerical method to simulate outcomes which we have been obtained,and give sensitivity analysis of some parameters.In Chapter 3,we consider a TB model with relapse and media coverage.First,By means of the next-generation matrix,the basic reproductive number R₀ is calculated.Then when R₀<1,we get the local and the global asymptotic stability of the disease-free equilibrium P0.Second,when R0>1,we prove the unique existence of the endemic equilibrium P^*.The stability of the endemic equilibrium P^*is obtained through numerical simulation.Further-more,the optimal control of TB vaccination and treatment is obtained by the Pontryagin's Maximum Principle.Finally,we use numerical simulations to verify the theoretical results.