Dynamics Of A Periodic Dengue Disease Transmission Model With Vaccination And Two Time Delays

In this paper,we propose a periodic dengue disease transmission model with vaccination and two time delays.We first introduce the basic reproduction ratio R₀ for this model and then prove that R₀ serves as a threshold value for the global extinction and uniform persistence of the disease.More precisely,the disease will die out if R₀<1;the system admits a positive periodic solution and the disease will persist if R₀>1.Numerically,we derive the algorithm to compute R₀ and study the dengue transmission case in Brazil.Our numerical simulation results are consistent with the theoretical results that we have obtained.In addition,we analyze the effects of the vaccination on the transmission of dengue and suggest the strategies to the prevention and control of dengue.