Abstract
A reaction-diffusion (R-D) heroin epidemic model with relapse and permanent immunization is formulated. We use the basic reproduction numberR0to determine the global dynamics of the models. For both the ordinary differential equation (ODE) model and the R-D model, it is shown that the drug-free equilibrium is globally asymptotically stable ifR0≤1, and ifR0>1, the drug-addiction equilibrium is globally asymptotically stable. Some numerical simulations are also carried out to illustrate our analytical results.
Highlights
Heroin comes from opioids, commonly known as “opium,” derived from the poppy plant
Since the spread of heroin is as contagious as infectious diseases, it is a new trend to study heroin transmission from the perspective of infectious disease dynamics [5,6,7,8,9,10,11,12,13,14,15,16]
In order to better study the dynamics of heroin infectious diseases, many other different epidemic models have been formulated and studied in various ways [5,6,7,8,9,10, 12, 13, 16]
Summary
Heroin comes from opioids, commonly known as “opium,” derived from the poppy plant. Pure heroin is a white powdery substance or a white crystalline powder. In order to better study the dynamics of heroin infectious diseases, many other different epidemic models have been formulated and studied in various ways [5,6,7,8,9,10, 12, 13, 16]. There are some people who have been well educated since childhood and have a healthy living environment and strong willpower They do not take drugs from the start to the finish. In the case of the heroin epidemic model, the spatial distribution of the susceptible or infected person is uneven, and the density may change at any time and place, it is more reasonable to use the R-D equations to describe the spread of drug abusers.
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