Dynamic Studies And Optimal Control Of Two Types Of TB

TB is a respiratory infection caused by Mycobacterium TB,which not only causes great losses to the economy,but also causes great harm to human life and health.TB has been listed as an infection that needs important control by the World Health Organization.As one of the countries with a high incidence of TB,China has about 130,000 deaths due to TB every year,which is second only to India in severity,so we must pay attention to the research and prevention and control of TB.It is one of the main methods of scholars to establish a suitable mathematical model to study it.Therefore,this paper builds the dynamic models of two types of TB on the basis of the previous work.This paper is divided into four chapters.The first chapter is the introduction,which introduces the background knowledge of TB,the current research status at home and abroad,and the preliminary knowledge used in this paper.In Chapter 2,we study a TB transmission dynamics model with the proportional input.Firstly,we obtain the basic reproduction ratio by using the next generation matrix.Secondly,we prove stability of equilibrium by Lyapunov functions and La Salle’s invariance principle,and by applying the optimal control theory,we obtain the existence and uniqueness of the optimal control solution and its expression.Finally,numerical simulations are presented to verify the above theoretical results,and we perform sensitivity analysis by Latin square sampling and partial rank correlation coefficient（PRCC）methods.In Chapter 3,we propose and analyze a TB transmission model that has nonlinear incidence rate and takes into account both immunization and medical treatment as effective intervention strategies.Firstly,the existences and stabilities of the equilibrium of the model are studied.The results indicate the disease-free equilibrium is globally asymptotically stable when ₀R（27）1,and the disease will gradually disappear.The only positive equilibrium is globally asymptotically stable when ₀R（29）1,and the disease will persist.Secondly,optimal control is added to the original model because of limited resources.Finally,the stability of the equilibrium and the theoretical results of optimal control are verified by numerical simulations,and the rationality of the model was verified with the actual data of TB in recent years.In chapter 4,summary and prospect.We summarize the current research work and point out the direction for future study.The final research results can provide effective strategies for prevention and control of TB.