A mathematical model to study the 2014–2015 large-scale dengue epidemics in Kaohsiung and Tainan cities in Taiwan, China

Dengue virus (DENV) infection is endemic in many places of the tropical and subtropical regions, which poses serious public health threat globally. We develop and analyze a mathematical model to study the transmission dynamics of the dengue epidemics. Our qualitative analyzes show that the model has two equilibria, namely the disease-free equilibrium (DFE) which is locally asymp- totically stable when the basic reproduction number ($\mathcal{R}_0$) is less than one and unstable if $\mathcal{R}_0$ > 1, and endemic equilibrium (EE) which is globally asymp-totically stable when $\mathcal{R}_0$ > 1. Further analyzes reveals that the model exhibit the phenomena of backward bifurcation (BB) (a situation where a stable DFE co-exists with a stable EE even when the $\mathcal{R}_0$ < 1), which makes the disease control more diffi-cult. The model is applied to the real dengue epidemic data in Kaohsiung and Tainan cities in Taiwan, China to evaluate the fitting performance. We propose two reconstruction approaches to estimate the time-dependent $\mathcal{R}_0$, and we find a consistent fitting results and equivalent goodness-of-fit. Our findings highlight the similarity of the dengue outbreaks in the two cities. We find that despite the proximity in Kaohsiung and Tainan cities, the estimated transmission rates are neither completely synchronized, nor periodically in-phase perfectly in the two cities. We also show the time lags between the seasonal waves in the two cities likely occurred. It is further shown via sensitivity analysis result that proper sanitation of the mosquito breeding sites and avoiding the mosquito bites are the key control measures to future dengue outbreaks in Taiwan.