Study Of Dynamic Models Of Disease Transmission Between Two Populations

The spread of infectious disease process often have certain time lag, periodic and inter-activity. Many scholars have been in the study of infectious diseases within a single popula-tions spreading, and has obtained plentiful research results. But all things depending on each other and saving, disease will spread between population, the combining research of popula-tion ecology and epidemiology has a certain significance. Therefore, this article studies au-tonomous predator-prey model with time delay and vaccination infectious disease model at first, the threshold value determining the presence or absence of disease is obtained, using the method of linearization and Lyapunov functional methods gain on the global asymptotic stabil-ity of the disease-free equilibrium and the local asymptotic stability of the endemic equilibrium. Using comparison principle and persistence to get sufficient conditions for the persistence of the model, and through the numerical simulation shows the establishment of the conclusion. Sec-ondly, on the basis of the previously discussed, we consider the impact on time factor for the model parameter, further discuss the non-autonomous SIRS predator-prey infectious disease model of time-delay and vaccination with nonlinear incidence on paper. By using comparison principle and method of Lyapunov functional getting global-attractivity of the model and ade-quacy criterion of continue and extinction with infectious diseases, and numerical simulation and theoretical conclusion in full accord. Last,state dependent pulse model of media trans-mission are studied in this paper, using analytic method and characteristic root method of the differential equation prove the stability of equilibrium on the impulse-free model, more, using the poincare mapping principle, poincare criteria respectively discuss the existence of periodic solutions and the asymptotic stability of trajectory for model, and the corresponding numerical simulation results show that order a periodic solution of the model is trajectory asymptotically stable.