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 $R_0$ of the model is defined. It is proved that the disease-free equilibrium is stable when $R_0<1$ and the positive equilibrium is stable when $R_0>1$. Next, we derive an estimation formula for the reproduction number $R_t$ when the human population is partially susceptible to dengue. As an application, the $R_t$ values of dengue transmission in Singapore in the years 2013–2015 are estimated. Our estimation method can be applied to estimating $R_t$ of other infectious diseases, especially when the human population is not completely susceptible to the disease.

在本文中，我们建立了具有两个延迟的数学模型，以反映登革热传播中病毒的内在和外在潜伏期。基本复制数${\mathrm{[R}}_0$模型的定义。证明了在以下情况下无病平衡是稳定的${\mathrm{[R}}_0<\mathrm{1个}$ 当以下情况时，正平衡是稳定的 ${\mathrm{[R}}_0>\mathrm{1个}$。接下来，我们得出再现次数的估计公式${\mathrm{[R}}_{Ť}$当人口部分易患登革热时。作为应用，${\mathrm{[R}}_{Ť}$估计了2013-2015年新加坡的登革热传播值。我们的估计方法可以应用于估计${\mathrm{[R}}_{Ť}$其他传染病，尤其是当人口不完全易感时。