Dynamics Of A Periodic Epidemic Model With Nonlinear Incidence Rate And Time Delay

In this paper,we study a periodic epidemic model with nonlinear incidence rate and time delay.We also give the theorems of the basic reproduction number R₀ to determine whether the disease exists or not.To consider the global dynamics,we establish sufficient conditions for the global extinction and uniform persistence of the disease in terms of the basic reproduction number,i.e.,if R₀<1,the disease-free equilib-rium is globally attractive;while the system admits a positive periodic solution and the disease is uniformly persistent if R₀>1.At last,we apply the numerical simulations to illustrate the theoretical results and to investigate the dependence of basic reproduction number on the relevant parameters and the amplitude of fluctuations.