Dengue transmission: mathematical model with discrete time delays and estimation of the reproduction number.

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. [ABSTRACT FROM AUTHOR]