| The prevention and control of infectious diseases is a major problem related to human health,national economy and people's livelihood.Mathematical modeling is one of the important methods to study the occurrence and change of infectious diseases.In some cases,impulsive differential equation models are more realistic than the corresponding impulseless differential equation models in studying laws and trends of disease transmissions.This paper is divided into two parts to study the infectious disease models with pulse effect and delays.In the first part,we study an SIRS epidemic model with pulse vaccination,birth pulse and Logistic death rate.By using the stroboscopic map of a discrete dynamical system,the disease-free periodic solution(DFPS for short)of the model under pulse vaccination and birth pulse is obtained.Based on the Floquet theory and comparison theorem of impulsive differential equations,the global asymptotic stability of the DFPS is given,and sufficient conditions for the permanence of the model are obtained.In addition,partial rank correlation coefficients(PRCC)method is used to analyze the sensitivity of each parameter on the threshold.Finally,numerical simulations are carried out by means of MATLAB programming,which shows the consistency on the numerical simulation results and the theoretical results.In the second part,we study an SEIRS epidemic model with pulse vaccination and two time delays.By using stroboscopic map of a discrete dynamical system and comparison principle,the disease-free periodic solution(DFPS for short)is.obtained and the global asymptotic stability of the DFPS is proved.The sufficient conditions for the permanence of the model are obtained.In addition,partial rank correlation coefficients(PRCC)method is used to analyze the sensitivity of each parameter on the threshold.Finally,numerical simulations are carried out by means of MATLAB programming,which shows the consistency on the numerical simulation results and the theoretical results. |
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