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 $ R_0 $ of the model is defined. It is proved that the disease-free equilibrium is stable when $ R_0 \lt 1 $ and the positive equilibrium is stable when $ R_0 \gt 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.

Keywords

• dengue transmission
• mathematical model
• delay
• reproduction number
• stability
• estimation