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

Abstract

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 R0 of the model is defined. It is proved that the disease-free equilibrium is stable when R0<1 and the positive equilibrium is stable when R0>1. Next, we derive an estimation formula for the reproduction number Rt when the human population is partially susceptible to dengue. As an application, the Rt values of dengue transmission in Singapore in the years 2013–2015 are estimated. Our estimation method can be applied to estimating Rt of other infectious diseases, especially when the human population is not completely susceptible to the disease.