The Study Of Stability Of Two Classes Of Infectious Disease Dynamics Model

The dynamics of infectious diseases is an important method to study the theory ofquantitative of infectious disease. According to the characteristics of the growth of popula-tion, the occurrence of the disease and spread in the population,the law of development andthe related social factors,we establish the mathematical model which can reaction kineticsto realize the study of infectious diseases.Currently, The current research on infectious dis-ease dynamics model is to study the stability of the equilibrium point in the system.In thispaper,we mainly studies the stability of two kinds infectious disease model: one kind is thedynamics model with vaccination and treatment, another kind is the dynamics model withtime delay.In chapter2, we mainly relate and analyze how to choose the appropriate treatmentfunction that combine with the practical, and by choosing the appropriate parameters toselect the Lyapunov function of the model, and to introduced the proof of the global stabilityof the equilibrium point.In chapter3, we mainly study the SVIR model with immune and treatment, the ba-sic reproduction number and equilibrium conditions are obtained, the global stability ofthe disease-free equilibrium and the endemic equilibrium point is proved by the Lyapunovfunction. Finally,we confrmed the steady state of equilibrium point by using the numericalsimulation.In chapter4,we mainly study the SIR epidemic model with time delay and nonlinearincidence, the basic reproductive number is obtained, and the disease free equilibrium andthe endemic equilibrium existence is proved, we prove the global stability of the disease-freeequilibrium and the endemic equilibrium point. The last, we confrmed that the time delayin this model will not infuence the spread of the disease by numerical simulation.