The Long Time Behavior Of Solutions For Infectious Disease Dynamics Of The Ordinary Differential Equation Model

In this thesis, we first study the non-negativity and global existence of the solutionsfor the infectious disease ODE model with three systems and four systems, then applyingthe basic theorem of the secondА.М.ЛяпуновLiapunov function and the Routh-Hurwitz criterion methods to study the conditions of the stability and asymptotic stabilityof the nonnegative steady solutions for the ODE systems. The result of the thesis has someguide meaning for the prediction and controlling of infectious disease.The whole paper consists of four chapters. In the first chapter, we brie?y introducesome background about the infectious disease model and the main results. In the secondchapter, we prove the non-negativity, the global existence and uniqueness of the solutionsfor the infectious disease model (1.1) and (1.2). In the third and fourth chapters, we provethe stability and asymptotic stability of the nonnegative steady solutions for the infectiousdisease model (1.1) and (1.2), respectively.