In this paper, we establish a mathematical model with two delays to reflect the intrinsic and extrinsic incubation periods of virus in dengue transmission. The basic reproduction number [Formula: see text] of the model is defined. It is proved that the disease-free equilibrium is stable when [Formula: see text] and the positive equilibrium is stable when [Formula: see text]. Next, we derive an estimation formula for the reproduction number [Formula: see text] when the human population is partially susceptible to dengue. As an application, the [Formula: see text] values of dengue transmission in Singapore in the years 2013-2015 are estimated. Our estimation method can be applied to estimating [Formula: see text] of other infectious diseases, especially when the human population is not completely susceptible to the disease.
Keywords: Dengue transmission; delay; estimation; mathematical model; reproduction number; stability.