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Title: A mathematical model to study the 2014–2015 large-scale dengue epidemics in Kaohsiung and Tainan cities in Taiwan, China
Authors: Musa, SS 
Zhao, S 
Chan, HS 
Jin, Z
He, D 
Keywords: Backward bifurcation
Dengue virus
Mathematical modelling
Stability analysis
Issue Date: 2019
Publisher: American Institute of Mathematical Sciences
Source: Mathematical biosciences and engineering, 2019, v. 16, no. 5, p. 3841-3863 How to cite?
Journal: Mathematical biosciences and engineering 
Abstract: 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 asymptotically stable when the basic reproduction number (R 0 ) is less than one and unstable if R 0 > 1, and endemic equilibrium (EE) which is globally asymptotically stable when 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 R 0 < 1), which makes the disease control more difficult. 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 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.
ISSN: 1547-1063
DOI: 10.3934/mbe.2019190
Rights: © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (
The following publication Salihu Sabiu Musa, Shi Zhao, Hei-Shen Chan, Zhen Jin, Daihai He. A mathematical model to study the 2014–2015 large-scale dengue epidemics in Kaohsiung and Tainan cities in Taiwan, China. Mathematical Biosciences and Engineering, 2019, 16(5): 3841-3863 is available at
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