Global Stability And Resistance For Three Infectious Diseases Models

It is immoral and unrealistic to do experiments of infections dieases in the crowd.So using model analysis and computer simulation for experiments is very important.But we usually consider the deterministic model, that is the model which describethe certain parameters by di?erence, di?erential, integral or functional di?erential e-quation, when establish the infectious dieases models. To a certain extent, they canreflect phenomenon approximately. In this thesis, a mathematical model for the trans-mission of Toxoplasmosis disease in human and cat populations with vaccination andtreatment is proposed and analyzed. Then, we consider the stability and uniformlypersistent of a model for the formation of resistant bacteria with double delays. Atlast, a model about pregnant woman and fetus infected both by susceptible bacteriaand resistant bacteria is presented. Numerical simulation and sensitivity analysis arealso conducted to con?rm and extend the analytic results.In Chapter 1, we mainly introduce the background and development situation ofthe subject, and give some theoretical tools and preliminaries serving the discussionin the paper.In Chapter 2, a mathematical model for the transmission of Toxoplasmosis dis-ease in human and cat populations with vaccination and treatment is proposed andanalyzed. Qualitative dynamics of the model is determined by the basic reproductionnumber R0. Then we prove the global stability of the disease-free equilibrium by con-structing Liapunov functions and uniform persistence of Toxoplasmosis disease. Atlast, an example is given to explain our conclusions. At the same time, some controlstrategies to reduce toxoplasmosis prevalence are also given.In Chapter 3, the global stability of a mathematical model with double delays forthe formation of resistant bacteria is analyzed. We also obtain the basic reproductionnumberR0. The globally asymptotically stable of endemic equilibrium is proved byLiapunov function method. At the same time, some numerical examples are given toexplain our conclusions.In Chapter 4, A model about pregnant woman and fetus infected both by suscep-tible bacteria and resistant bacteria is presented. Qualitative analysis of the modelabout positivity,boundedness, global stability and uniform persistence is carried out.Analytic results show that antibiotic input has potential impact for neonatal drug re-sistance. Numerical simulation and sensitivity analysis are also conducted to con?rmand extend the analytic results.