Browsing by Author "Khalil M."

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Backward bifurcation in a fractional order epidemiological model
(Natural Sciences Publishing, 2017) El-Sayed A.M.A.; Arafa A.A.M.; Khalil M.; Sayed A.; Department of mathematics; Faculty of Science; Alexandria University; Alexandria; Egypt; Department of Mathematics; Faculty of Science; Port Said University; Port Said; Egypt; Department of Mathematics; Faculty of Engineering; October University for Modern Sciences and Arts (MSA University); Giza; Egypt
An epidemiological fractional order model which displays backward bifurcation for some parameters values, is studied in this paper. Because integer order of such model does not convey any information about the effect of the memory or learning mechanism of human population which influences disease transmission, we use the fractional order model in which the memory effect is considered well. As the fractional derivative is considered as the memory index, so the goal of this paper is to study the impact of fractional order derivative on the backward bifurcation phenomenon and on the basic reproduction number R0. � 2017 NSP.
The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional order model
(2013) Arafa A.A.M.; Rida S.Z.; Khalil M.; Department of Mathematics; Faculty of Science; South Valley University; Qena; Egypt; Department of Mathematics; Faculty of Engineering; Modern Science and Arts University (MSA); Giza; Egypt
In this paper, generalized Euler method (GEM) and homotopy analysis method (HAM) are performed to solve the problem of the population dynamics of the human immunodeficiency type 1 virus (HIV-1). We introduce fractional orders to the model of HIV-1 whose components are plasma densities of uninfected CD4+ T-cells, the infected such cells and the free virus. The effect of the drug treatment of HIV-1 will be discussed in this paper. � 2012 Elsevier Inc.
Fractional modeling dynamics of HIV and CD4 +T-cells during primary infection
(2012) Arafa A.A.M.; Rida S.Z.; Khalil M.; Department of mathematics; Faculty of Science; South Valley University; Qena; Egypt; Department of mathematics; Faculty of Engineering; Modern Science and Arts University (MSA); Giza; Egypt
In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4 +T cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model. � 2012 Arafa et al; licensee BioMed Central Ltd.
A fractional-order model of HIV infection: Numerical solution and comparisons with data of patients
(World Scientific Publishing Co. Pte Ltd, 2014) Arafa A.A.M.; Rida S.Z.; Khalil M.; Department of Mathematics and Computer Science; Faculty of Sciences; Port Said University; Port Said; Egypt; Department of Mathematics; Faculty of Sciences; South Valley University; Qena; Egypt; Department of Mathematics; Faculty of Engineering; October University for Modern Sciences and Arts; 6th Oct. City; Giza; Egypt
In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus (HIV-1) infection is presented. Numerical solutions are obtained using a generalized Euler method (GEM) to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These comparisons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model. � 2014 World Scientific Publishing Company.
Mathematical model of vector-borne plant disease with memory on the host and the vector
(Natural Sciences Publishing, 2016) Rida S.Z.; Khalil M.; Hosham H.A.; Gadellah S.; Department of Mathematics; Faculty of Science; South Valley University; Qena; Egypt; Department of Mathematics; Faculty of Engineering; Modern Science and Arts University (MSA); Giza; Egypt; Department of Mathematics; Faculty of Science; Al Azhar University; Assiut; Egypt
In this paper, we introduce a fractional order model of vector-borne plant diseases. Memory in both the host, and the vector population provides essential tools to understand the behavior of plant diseases. We use the presented model to study the effects of memory on the host and the vector. The fractional order derivative which is considered as the index of memory is described in the Caputo sense. � 2016 NSP.
A mathematical model with memory for propagation of computer virus under human intervention
(Natural Sciences Publishing, 2016) El-Sayed A.A.M.; Arafa A.A.M.; Khalil M.; Hassan A.; Department of Mathematics; Faculty of Science; Alexandria University; Alexandria; Egypt; Department of Mathematics; Faculty of Science; Port Said University; Port Said; Egypt; Department of Mathematics; Faculty of Engineering; October University forModern Sciences and Arts(MSA University); Giza; Egypt; Department of Science and Mathematical Engineering; Faculty of Petroleum and Mining Engineering; Suez University; Suez; Egypt
In this paper, we propose a fractional order model for the propagation behavior of computer virus under human intervention to study the spread of computer virus across the internet. Numerical simulations are used to show the behavior of the solutions of the proposed fractional order system. � 2016 NSP.
A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay
(Hindawi Limited, 2019) Arafa A.A.M.; Khalil M.; Sayed A.; Department of Mathematics and Computer Science; Faculty of Science; Port Said University; Port; Egypt; Department of Mathematics; Faculty of Engineering; October University for Modern Sciences and Arts (MSA); Giza; Egypt
The purpose of this paper is to propose a variable fractional-order model with a constant time delay of the coinfection of HIV/AIDS and malaria. The proposed model describes the interaction between HIV/AIDS and malaria. This model is presented by using variable fractional-order derivative which is an extension of the constant fractional-order derivative to explain a certain pattern in the development of infection of several patients. The presented model has been solved numerically via the predictor-corrector scheme. The local and global stability conditions of the disease-free equilibrium are investigated. Also, numerical simulations are presented for different variable fractional-order derivatives in Caputo sense. � 2019 A. A. M. Arafa et al.