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Global dynamics of an age-structured viral infection model with general incidence function and absorption

International Journal of Biomathematics 2018年第5期11卷 93-110页

作者： khalid hattaf Yu Yang Centre Regional des Mdtiers de l'Education et de la Formation (CRMEF) 20340 Derb Ghalef Casablanca Morocco School of Science and Technology Zhejiang International Studies University Hangzhou 310023 P. R. China

In this paper, we propose an age-structured viral infection model with general incidence function that takes account of the loss of viral particles due to their absorption into susceptible cells. The proposed model is described by partial differential and ordinary differential equations. We first show that the model is mathematically and biologically well-posed. Furthermore, the uniform persistence and the global behavior of the model are investigated. Moreover, the age-structured models and results presented in many previous studies are improved and generalized.

关键词： Age of infection general incidence function global stability

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Modeling the dynamics of COVID-19 with carrier effect and environmental contamination

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第3期12卷 167-182页

作者： khalid hattaf Ahmed A.Mohsen Jamal Harraq Centre Regional des M´etiers de l’Education et de la Formation(CRMEF)20340 Derb Ghalef CasablancaMorocco Laboratory of Analysis Modeling and Simulation(LAMS)Faculty of Sciences Ben M’sik Hassan II University of Casablanca P.O.Box 7955 Sidi Othman Casablanca Morocco Department of Mathematics College of Education for Pure Science(Ibn Al-Haitham)University of Baghdad Iraq Ministry of Education Rusafa 1BaghdadIraq

Nowadays,coronavirus disease 2019(COVID-19)poses a major threat to humanity which is caused by a novel coronavirus in Wuhan,China,at the end of December *** novel coronavirus named the severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)according to the International Committee on Taxonomy of Viruses(ICTV).It spreads directly through close contact with an asymptomatic(carrier)or symptomatic person who is coughing,sneezing,talking,singing and *** also spreads indirectly through contact with an environment contaminated by viral particles of *** the absence of effective treatment against COVID-19,awareness can play an important role in reducing cases of *** this study,we develop a mathematical model to better describe the dynamics of COVID-19 by taking into account the above modes of transmission and the prosocial *** existence,uniqueness,positivity and boundedness of solutions of the model are *** possible equilibrium points are *** local asymptotic stability of these equilibrium points is *** Lyapunov functionals are constructed to investigate the global dynamics of the model.

关键词： COVID-19 awareness asymptomatic people environmental transmission mathematical modeling

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Stability of HIV-1 infection with saturated virus-target and infected-target incidences and CTL immune response

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International Journal of Biomathematics 2017年第5期10卷 209-237页

作者： A. M. Elaiw A. A. Raezah khalid hattaf Department of Mathematics Faculty of Science King Abdulaziz University Jeddah P. O. Box 80203 21589 Saudi Arabia Centre Regional des Metiers de l'Education et de la Formation (CRMEF) Casablanca 20340 Derb Ghalef Morocco

This paper studies the dynamical behavior of an HIV-1 infection model with satu- rated virus-target and infected-target incidences with Cytotoxic T Lymphocyte （CTL） immune response. The model is incorporated by two types of intracellular distributed time delays. The model generalizes all the existing HIV-1 infection models with cell-to- cell transmission presented in the literature by considering saturated incidence rate and the effect of CTL immune response. The existence and global stability of all steady states of the model are determined by two parameters, the basic reproduction number （R0） and the CTL immune response activation number （R1）. By using suitable Lyapunov functionals, we show that if R0≤1, then the infection-free steady state So is globally asymptotically stable; if R1≤1〈R0, then the CTL-inactivated infection steady state S1 is globally asymptotically stable; if R1〉1, then the CTL-activated infection steady state S2 is globally asymptotically stable. Using MATLAB we conduct some numerical simulations to confirm our results. The effect of the saturated incidence of the HIV-1 dynamics is shown.

关键词： HIV-1 dynamics global stability time delay cell-to-cell transfer CTL immune response.

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