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Backward,Hopf bifurcation in a heroin epidemic model with treat age

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第2期12卷 198-222页

作者： Soufiane Bentout salih djilali Behzad Ghanbari Laboratoire d’Analyse Non Lin´eaire et Math´ematiques Appliqu´ees Universit´e de Tlemcen TlemcenAlgeria Department of Basic Science Kermanshah University of Technology KermanshahIran Faculty of Exact and Computer Sciences Mathematic Department Hassiba Benbouali UniversityChlefAlgeria §Department of Mathematics and Informatics Belhadj Bouchaib University Center of Ain Temouchent BP 284 RP 46000Algeria

Heroin is considered as damage on the health of the *** this paper,we consider a heroin epidemic model with treat age,where the inner rivalry in between the drug users for a small dose of drugs is *** influence of treatment period for a drug consumer before quitting treatment is investigated,where it is obtained that the considered model can undergo backward bifurcation,which shows the possibility of having two endemic equilibriums,this type of bifurcation is discussed in terms of the basic reproduction number *** bifurcation diagram is drown in the case of an age structured ***,we show the existence of Hopf bifurcation is shown under suitable conditions on the model *** obtained mathematical results are confirmed numerically.

关键词： Backward bifurcation heroin epidemic age-structured model Hopfbifurcation

Global threshold dynamics of an age structured alcoholism model

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International Journal of Biomathematics 2021年第3期14卷 153-186页

作者： Soufiane Bentout salih djilali Abdenasser Chekroun Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées University of TlemcenTlemcen 13000Algeria Department of Mathematics and Informatics Belhadj Bouchaib University Center of Ain TemouchentAin Temouchent 46OOOAlgeria Faculty of Exact and Computer Sciences Mathematic DepartmentHassiba Benbouali UniversityChiefAlgeria University of Abou Bekr Belkaid Tlemcen Tlemcen 13000Algeria

We consider in this research an age-structured alcoholism *** global behavior of the model is *** is proved that the system has a threshold dynamics in terms of the basic reproduction number(BRN),where we obtained that alcohol-free equilibrium(AFE)is globally asymptotically stable(GAS)in the case R_(0)≤1,but for R_(0)>1 we found that the system persists and the nontrivial equilibrium(EE)is ***,the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated,which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied *** obtained mathematical results are tested numerically next to its biological relevance.

关键词： Mathematical biology age-structured partial differential equations alcohol model uniform persistence global behavior Lyapunov function

Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix

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International Journal of Modeling, Simulation, and Scientific Computing 2022年第1期13卷 251-264页

作者： Rachid Belgacem Ahmed Bokhari salih djilali Sunil Kumar Faculty of Exact and Computer Sciences Mathematic Department Hassiba Benbouali UniversityChlefAlgeria Laboratory of Mathematics and its Applications(LMA)Faculty of Exact and Computer Sciences Hassiba Benbouali University ChlefAlgeria Laboratoire d’Analyse Non Lineaire et Mathematiques Appliquees Universite de Tlemcen TlemcenAlgeria Department of Mathematics National Institute of Technology Jamshedpur 831014JharkhandIndia

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational *** efficiency of the presented approach is demonstrated by solving some differential ***,this technique is combined with the standard Laplace Homotopy Per-turbation *** numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

关键词： Laplace transform Boubaker polynomials operational matrix homotopy per-turbation method numerical method

Impact of predation in the spread of an infectious disease with time fractional derivative and social behavior

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第4期12卷 92-119页

作者： Soufiane Bentout Behzad Ghanbari salih djilali Lakshmi Narayan Guin Department of Mathematics and Informatics Belhadj Bouchaib University Center of Ain Temouchent BP 284 RP 46000Algeria Laboratoire d’Analyse Non Linaire et Mathmatiques Appliques Universit de Tlemcen TlemcenAlgeria Department of Engineering Science Kermanshah University of Technology KermanshahIran Department of Biomedical Engineering Faculty of Engineering and Naturel Sciences Bah¸ce¸sehir University 34349 IstanbulTurkey Faculty of Exact and Computer Sciences Mathematic Department Hassiba Benbouali University ChlefAlgeria Department of Mathematics Visva-Bharati Santiniketan-731235 West BengalIndia

The main purpose of this paper is to explore the influence of predation on the spread of a disease developed in the prey population where we assume that the prey has a social *** memory of the prey and the predator measured by the time fractional derivative plays a crucial role in modeling the dynamical response in a predator–prey *** memory can be modeled to articulate the involvement of interacting species by the presence of the time fractional derivative in the considered *** the purpose of studying the complex dynamics generated by the presence of infection and the time-fractional-derivative we split our study into two cases. The first one is devotedto study the effect of a non-selective hunting on the spread of the disease, where the localstability of the equilibria is investigated. Further the backward bifurcation is obtainedconcerning basic reproduction rate of the infection. The second case is for explaining theimpact of selecting the weakest infected prey on the edge of the herd by a predator onthe prevalence of the infection, where the local behavior is scrutinized. Moreover, for thegraphical representation part, a numerical simulation scheme has been achieved usingthe Caputo fractional derivative operator.

关键词： Predator–prey model herd behavior fractional derivative numerical schema backward bifurcation eco-epidemiological model

Pattern dynamics of a reaction-diffusion predator-prey system with both refuge and harvesting

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International Journal of Biomathematics 2021年第1期14卷 1-29页

作者： Lakshmi Narayan Guin Sudipta Pal Santabrata Chakravarty salih djilali Department of Mathematics Visva-BharatiSantiniketan 731235West BengalIndia Department of Mathematics Universite Hassiba Benbouali de ChlefChlef 02000Algeria Laboratoire d’Analyse Non Linéaire et Mathématiques AppliquéesUniversitéde TlemcenTlemcenAlgeria

We are concerned with a reaction-diffusion predator–prey model under homogeneous Neumann boundary condition incorporating prey refuge(proportion of both the species)and harvesting of prey species in this *** for asymptotic stability(local and global)and bifurcation of the subsequent temporal model system are thoroughly analyzed around the unique positive interior equilibrium *** partial differential equation(PDE),the conditions of diffusion-driven instability and the Turing bifurcation region in two-parameter space are *** results around the unique interior feasible equilibrium point specify that the effect of refuge and harvesting cooperation is an important part of the control of spatial pattern formation of the species.A series of computer simulations reveal that the typical dynamics of population density variation are the formation of isolated groups within the Turing space,that is,spots,stripe-spot mixtures,labyrinthine,holes,stripe-hole mixtures and stripes ***,we discuss spatiotemporal dynamics of the system for a number of different momentous parameters via numerical simulations.

关键词： Two species reaction-diffusion system ratio-dependent functional response diffusion-driven instability pattern selection stationary patterns