Analysis of a Diffusive Heroin Epidemic Model in a Heterogeneous Environment. (20th May 2020)

• Record Type: Journal Article
• Authors: Wang, Jinliang; Sun, Hongquan
• Other Names: Wei Yan-Ling Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-05-20
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/8268950
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : This paper is concerned with a reaction-diffusion heroin model in a bound domain. The objective of this paper is to explore the threshold dynamics based on threshold parameter and basic reproduction number (BRN) ℜ 0, and it is proved that if ℜ 0 < 1, heroin spread will be extinct, while if ℜ 0 > 1, heroin spread is uniformly persistent and there exists a positive heroin-spread steady state. We also obtain that the explicit formula of ℜ 0 and global attractiveness of constant positive steady state (PSS) when all parameters are positive constants. Our simulation results reveal that compared to the homogeneous setting, the spatial heterogeneity has essential impacts on increasing the risk of heroin spread.