Qualitative Theory Analysis Of Two Types Of Infectious Diseases

Epidemic dynamics is to study disease spread, predict the trends of the disease,?nd out the key factors in the process of the spread, and prevent the disease by the best methods. Based on this fact, we mainly investigate the stability of a delayed SIR model with general nonlinear incidence and multiple parallel infectious stages,and the existence of travelling wave solutions in delayed reaction di?usion systems with partial exponential non-quasimonotonicity.For the delayed SIR model with general nonlinear incidence and multiple parallel infectious stages, we obtain equilibrium points of the model and the basic reproductive number ?0, and then study the global stability of the equilibrium points by constructing appropriate Lyapunov functions. If ?0≤ 1, the disease-free equilibrium is globally asymptotically attractive. If ?0> 1, the endemic equilibrium is globally asymptotically attractive. For the delayed reaction di?usion systems with partial exponential non-quasimonotonicity, we build some auxiliary lemmas, and then give the existence theorem of travelling wave solutions for the system according to Schauders ?xed point theorem.Using the method of uniform persistence theory to determine the stability criterion for uniform persistence model and all equilibriums, obtaining threshold dynamics of disease transmission in the long time, and applying it to more infectious disease transmission model, are very meaningful work both in the theory of stability and in disease control and prevention.