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238 results on '"Djilali, Salih"'

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

Author

Djilali, Salih, Loumi, Amine, Bentout, Soufiane, Sarmad, Ghilmana, and Tridane, Abdessamad

Subjects
*BASIC reproduction number, *DELAY differential equations, *DRUG addiction, *SOCIAL impact, *ECONOMIC impact, *HEROIN
Abstract

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 R0$$ {\mathfrak{R}}_0 $$, 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 R0<1$$ {\mathfrak{R}}_0<1 $$. If R0>1$$ {\mathfrak{R}}_0>1 $$, 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 R0$$ {\mathfrak{R}}_0 $$ below one. [ABSTRACT FROM AUTHOR]

Published
2024
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27. Dynamics of a delayed nonlocal reaction–diffusion heroin epidemic model in a heterogenous environment.

Author

Djilali, Salih, Chen, Yuming, and Bentout, Soufiane

Subjects
*BASIC reproduction number, *HEROIN, *SPECTRAL theory, *EPIDEMICS
Abstract

To study the consumption of heroin in a heterogeneous environment, we propose and analyze a spatiotemporal model with a distributed delay. Using the spectral theory, we determine the basic reproduction number R0$$ {R}_0 $$, which serves a threshold role. If R0<1$$ {R}_0<1 $$, then the addiction‐free steady state is globally asymptotically stable while if R0>1$$ {R}_0>1 $$, then there is at least one addictive steady state. Moreover, when R0>1$$ {R}_0>1 $$, if one of the dispersal coefficients is zero, then there is only one addictive steady state, and it is globally asymptotically stable; if both diffusions of susceptible and addicted individuals are present, we cannot identify the temporal behavior of solutions, and hence, we study the asymptotic profile of addictive steady states when one of the dispersal coefficients tend to zero. [ABSTRACT FROM AUTHOR]

Published
2024
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41. New generalized integral transform via Dzherbashian-Nersesian fractional operator.

Author

Belgacem, Rachid, Bokhari, Ahmed, Baleanu, Dumitru, and Djilali, Salih

Subjects
GENERALIZED integrals, INTEGRAL transforms, FRACTIONAL differential equations
Abstract

In this paper, we derive a new generalized integral transform on Dzherbashian-Nersesian fractional operator and give some special cases. We make a generalization of the application of integral transformations to different fractional operators, where several previous results can be invoked from a single relation. We also use the new results obtained to solve some fractional differential equations involving the recent revival of Dzherbashian-Nersesian fractional operators. [ABSTRACT FROM AUTHOR]

Published
2024
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