Dynamics of a dengue fever transmission model with crowding effect in human population and spatial variation
type: Item
instance of: scholarly article
title: Dynamics of a dengue fever transmission model with crowding effect in human population and spatial variation
zbMATH Open document ID: 1284.35225
author: Tzy-Wei Hwang
author: Feng-Bin Wang
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2013-03-19T00:00:00Z
review text: Dengue fever is a virus-caused disease in the world. Since the high infection rate of dengue fever and high death rate of its severe form dengue hemorrhagic fever, the control of the spread of the disease is an important issue in the public health. In this paper, authors modify the autonomous system provided in reference [\textit{L. Esteva} and \textit{C. Vargas}, Math. Biosci. 150, No. 2, 131--151 (1998; Zbl 0930.92020)] to obtain a reaction-diffusion system with crowding effect in human population and spatial variation. Authors first study a heterogeneous model with a spatially variable habitat. By the theory of monotone dynamical systems and uniformly persistent, authors obtain threshold number that predicts the disease persistence or extinction. When all the coefficients are habitat independent (i.e. positive constants), the global attractiveness of the steady solutions is discussed by an appropriate Lyapunov function. These findings could be viewed as a generalization to those obtained in reference [loc. cit.]. It is interesting that this paper expounds how the spatial heterogeneity and crowding effect influence the dynamics of the spread of the disease.
reviewed by: Zhen Jin
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6146703
zbMATH Keywords: global stability
zbMATH Keywords: Lyapunov functional
zbMATH Keywords: extinction and persistence
zbMATH Keywords: basic reproduction number
zbMATH Keywords: monotone dynamical systems
MaRDI profile type: Publication
full work available at URL: dcdsb.2013.18.147
OpenAlex ID: W2312264388
DOI: 10.3934/DCDSB.2013.18.147
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description: scientific article; zbMATH DE number 6146703