A Time‐Delayed Dengue Transmission Model With Seasonal Variations

ABSTRACT In this paper, we propose a periodic dengue disease transmission model with two time delays (to describe the extrinsic and intrinsic incubation periods). We first introduce the basic reproduction ratio for this model and then prove that serves as a threshold value for the global extinction and uniform persistence of the disease. More precisely, the disease will die out if ; the system admits a positive periodic solution and the disease will persist if . Numerically, we derive an algorithm to compute and study the dengue transmission case in Thailand. Our numerical results are consistent with the theoretical results that we have obtained. In addition, we explore the dependence of on some important parameters.