Global dynamics of a discretized heroin epidemic model with time delay. (English) Zbl 1406.92547

Abdurahman, Xamxinur; Zhang, Ling; Teng, Zhidong

Abstr. Appl. Anal. 2014, Article ID 742385, 10 p. (2014).

Summary: We derive a discretized heroin epidemic model with delay by applying a nonstandard finite difference scheme. We obtain positivity of the solution and existence of the unique endemic equilibrium. We show that heroin-using free equilibrium is globally asymptotically stable when the basic reproduction number \(R_0 < 1\), and the heroin-using is permanent when the basic reproduction number \(R_0 > 1\).

MSC:

92D30	Epidemiology
34D23	Global stability of solutions to ordinary differential equations

Keywords:

heroin epidemic model; global asymptotic stability

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