Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity

Xu, Jin

doi:10.1080/17513758.2023.2189026

Journal of Biological Dynamics

2023

DOI: 10.1080/17513758.2023.2189026

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Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity

Jin Xu

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2024

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Cited by 3 publications

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Mathematical modeling of containing the spread of heroin addiction via awareness program

Djilali,

Loumi,

Bentout

et al. 2024

Math Methods in App Sciences

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As many countries are hit by the social economic impact of heroin addiction, there is an urgent need to have an effective awareness program that focuses on educating the population on the danger of heroin addiction and helping the heroin‐users quit. This paper aims to study the effect of the awareness program on the spread of heroin dependence using a mathematical model with distributed delay. First, we show the existence threshold parameter , which we call the basic reproduction number of the spread of heroin use. We prove, via the Lyapunov direct method, that the drug‐free equilibrium is globally asymptotically stable if . If , the drug dependence persists, and the drug equilibrium is globally asymptotically stable. We give three possible scenarios to find the optimal awareness program strategy that puts the heroin epidemic under control. These scenarios take into consideration the reachability of the population, the immunity against heroin addiction, and the effectiveness of the program to contain the use of heroin in the population and bring below one.

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Mathematical modeling of containing the spread of heroin addiction via awareness program

Djilali,

Loumi,

Bentout

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

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Global stability and modeling with a non-singular kernel for fractional order heroin epidemic model: Insights from different population studies

Vivas-Cortez,

Bakar,

Alqarni

et al. 2024

Journal of King Saud University - Science

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Coupling media coverage and susceptibility for modeling epidemic dynamics: An application to COVID-19

Wang,

Zhang

2024

Mathematics and Computers in Simulation

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Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity

Cited by 3 publications

References 37 publications

Mathematical modeling of containing the spread of heroin addiction via awareness program

Mathematical modeling of containing the spread of heroin addiction via awareness program

Global stability and modeling with a non-singular kernel for fractional order heroin epidemic model: Insights from different population studies

Coupling media coverage and susceptibility for modeling epidemic dynamics: An application to COVID-19

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