Study On Dynamic Analysis And Control Measures Of Several Types Of Tuberculosis Models

Tuberculosis is a chronic infectious disease caused by Mycobacterium tuberculosis,which seriously damages human health.In recent years,it has become a hot issue to study the spread and epidemic trends of infectious diseases by mathematical model.The research results provide a good theoretical basis for the prevention and control of infectious diseases.Based on the pathological characteristics and transmission mechanism of tuberculosis,the dynamics and control measures of several types of tuberculosis models were studied.First,a dynamic model of tuberculosis with optimal control measures was studied.A sensitivity analysis of the basic number of regeneration of the model shows that control measures are effective and it can reduce the spread of disease among people.In addition,it is discussed that under the optimal treatment control measures of non-resistance and drug resistance,the optimal control pair which minimizes makes the objective function exists.That is,when control measures are applied,the total number of people infected with M.tuberculosis(infected and latently infected)will decrease.Finally,numerical simulations were used to demonstrate the spread of disease under different intensity of control measures.Secondly,a dynamic model of tuberculosis with control measures,latent treatment and recurrence was established.The threshold is obtained by using the regenerative matrix method.The existence of the disease-free equilibrium point and the endemic disease equilibrium point are discussed.The condition of local stability of the disease-free equilibrium point when the basic regeneration number is less than 1 is given by using the Hurwitz criterion.The Morse decomposition theorem is used to discuss the condition.The consistent durability of the system when the number of basic regenerations is greater than one.Further,the control measures are applied to the model,and the optimal control pair minimizes the objective function.The numerical simulation also shows the spread of the disease under different control measures.Finally,a dynamic model for the treatment of patients with exogenous reinfection and latent infection was established.The existence and stability of the equilibrium point were discussed with given parameter values.Cross-critical bifurcation,saddle node bifurcation,and Hopf bifurcation that may occur at the equilibrium point are also discussed.