A periodic dengue transmission model with two time delays and vaccination: Application to dengue dynamics in Brazil

In this paper, we propose a periodic dengue disease transmission model with two time delays and vaccination. We first introduce the basic reproduction ratio [Formula: see text] for this model and then prove that [Formula: see text] serves as a threshold value for the global extinction and uniform persistence of the disease. More precisely, the disease will die out if [Formula: see text]; the system admits a positive periodic solution and the disease will persist if [Formula: see text]. Numerically, we derive the algorithm to compute [Formula: see text] 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 propose strategies for its prevention and control.