| In recent years, with the rapid development of researches on epidemic dynamics,large number of mathematical models are used to analyze various infectious diseasesin the world. It is s more reasonable and accurate to describe regular vaccinationwith impulsive di?erential equations than the corresponding models without pulsein epidemic models. What's more, regular vaccination is an e?ective way to controlinfectious diseases as well as eradication of infectious disease. The aim of this paper isto investigate the e?ect of latent period, infection period, immunity period, isolationmeasures, vertical transmission and other factors on infectious disease by researchon three kinds of pulse vaccination infectious disease models.Considering latent period and infection period and immunity period of thedisease, we investigate a pulse vaccination SEIRS epidemic model with multi-delayand nonlinear incidence rate at first. According to the theory of delay di?erentialequations and the comparison theorem of impulsive di?erential equations, we analyzethe global attractivity of infection-free periodic solution, and obtain a su?cientcondition for the permanence of disease. Theoretical results are verified throughnumerical simulations.Secondly, we study a kind of pulse vaccination SEIQRS epidemic models withquarantine measure and nonlinear incidence rate, and consider the e?ect of latentperiod, immunity period and isolations. The su?cient condition for existence ofinfection-free periodic solution, global attractivity and the permanence of the systemare obtained. Numerical simulations validate our results.Finally, considering the saturated incidence rate and vertical infection–anotherinfection way of infectious disease, a new SVIRS epidemic model with pulse vaccina-tion is studied. The infection-free periodic solution of the pulse discrete system andthe basic reproduction number are obtained by using the stroboscopic technologydetermined by discrete dynamical systems.
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