Modeling the effect of temperature on dengue virus transmission with periodic delay differential equations

Haitao Song; Dan Tian; Chunhua Shan; Haitao Song; Dan Tian; Chunhua Shan

doi:10.3934/mbe.2020230

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 4147-4164. doi: 10.3934/mbe.2020230

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Modeling the effect of temperature on dengue virus transmission with periodic delay differential equations

1.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
2.
Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on disease Control and Prevention, Shanxi University, Taiyuan 030006, China
3.
Department of Mathematics and Statistics, The University of Toledo, Toledo 43606, USA

Received: 08 April 2020 Accepted: 08 June 2020 Published: 12 June 2020

Dengue fever is a re-emergent mosquito-borne disease, which prevails in tropical and subtropical regions, mainly in urban and peri-urban areas. Its incidence has increased fourfold since 1970, and dengue fever has become the most prevalent mosquito-borne disease in humans now. In order to study the effect of temperature on the dengue virus transmission, we formulate a dengue virus transmission model with maturation delay for mosquito production and seasonality. The basic reproduction number $\mathbb{R}_0$ of the model is computed, and results suggest that the dengue fever will die out if $\mathbb{R}_0$ < 1, and there exists at least one positive periodic solution and the disease will persist if $\mathbb{R}_0$ > 1. Theoretical results are applied to the outbreak of dengue fever in Guangdong province, China. Simulations reveal that the temperature change causes the periodic oscillations of dengue fever cases, which is good accordance with the reported cases of dengue fever in Guangdong province. Our study contributes to a better understanding of dengue virus transmission dynamics and proves beneficial in preventing and controlling of dengue fever.
- dengue fever,
- temperature,
- maturation delay,
- seasonality,
- periodic solution,
- uniform persistence
Citation: Haitao Song, Dan Tian, Chunhua Shan. Modeling the effect of temperature on dengue virus transmission with periodic delay differential equations[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 4147-4164. doi: 10.3934/mbe.2020230

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Abstract

Dengue fever is a re-emergent mosquito-borne disease, which prevails in tropical and subtropical regions, mainly in urban and peri-urban areas. Its incidence has increased fourfold since 1970, and dengue fever has become the most prevalent mosquito-borne disease in humans now. In order to study the effect of temperature on the dengue virus transmission, we formulate a dengue virus transmission model with maturation delay for mosquito production and seasonality. The basic reproduction number $\mathbb{R}_0$ of the model is computed, and results suggest that the dengue fever will die out if $\mathbb{R}_0$ < 1, and there exists at least one positive periodic solution and the disease will persist if $\mathbb{R}_0$ > 1. Theoretical results are applied to the outbreak of dengue fever in Guangdong province, China. Simulations reveal that the temperature change causes the periodic oscillations of dengue fever cases, which is good accordance with the reported cases of dengue fever in Guangdong province. Our study contributes to a better understanding of dengue virus transmission dynamics and proves beneficial in preventing and controlling of dengue fever.

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