The Stability Analysis Of Several Types Of Tuberculosis Model With Incomplete Treatment

Tuberculosis is a chronic infectious disease caused by Mycobacterium.China is the hardest hit by the tuberculosis epidemic.Its severity is second only to India and Indonesia.What is even more serious is that China has the world's most multidrug-resistant TB population.Therefore,the study on the development of the tuberculosis epidemic cannot be delayed.In this paper,according to the influence of the uncertainty of pulmonary tuberculosis latency,population flow,vaccination and incomplete treatment on the spread of pulmonary tuberculosis,several types of tuberculosis model are established and the dynamics of the model are studied.In chapter two,the tuberculosis epidemic model with vaccination and incomplete treatment is established.The threshold for the extinction of pulmonary tuberculosis is obtained.The existence and stability of model equilibrium points10 E and1E(9)are analyzed.Through analysis,it is concluded that to control the disease,10 R can be reduced by strengthening the inoculation rate of newborns and susceptible people so as to control the spread of the disease.It is also possible to improve the effectiveness of treatment by developing effective drugs and improving patient compliance.The optimal control strategy of vaccination and treatment in pulmonary tuberculosis transmission model is analyzed by using the Pontryagin maximum principle.In chapter three,an incomplete treatement tuberculosis model with vaccination and rapid and slow progression is studied.And the threshold of extinction of tuberculosis is obtained.The stability of the equilibrium point of the pulmonary tuberculosis propagation model is determined by the Lyapunov function and La Salle invariant set principle.The correlation analysis showed that when there is20 R ?1,the model had a disease-free equilibrium point and the disease-free equilibrium is globally asymptotically stable.When20R>1,the model had a positive equilibrium point and a disease-free equilibrium point.The disease-free balance point is unstable,and the positive equilibrium point is globally asymptotically stable.And then verification and support of the theoretical results are made through numerical simulation.The influence of the length of pulmonary tuberculosis latency,the coefficient of treatment received,the successful treatment coefficient,and the patient's own self-immunity on the prevalence of pulmonary tuberculosis are analyzed.In chapter four,a tuberculosis transmission model with population flow and rapid progress is studied.Two thresholds are obtained and the stability of the equilibrium point of the model.When01 MR ? and01 PR ?,there is a disease-free equilibrium point in the model,and the disease-free equilibrium point is globally asymptotically stable;when01MR(29),the model has a positive equilibrium,and the positive equilibrium is locally asymptotically stable;when01MR ? and01PR(29),the model has a unique boundary equilibrium point,and the boundary equilibrium point is globally asymptotically stable.