Browsing by Author "Souleiman, Yahyeh"

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    Analysis the Dynamics of SIHR Model: Covid-19 Case in Djibouti
    (Applied Mathematics,, 2021-10-14) Souleiman, Yahyeh; Mohamed, Abdoulrazack; Ismail, Liban
    The Covid-19 epidemic is an emerging infectious disease of the viral zoonosis type caused by the coronavirus strain SARS-CoV-2, it is classified as a human-to-human communicable disease and is currently a pandemic worldwide. In this paper, we propose conceptual mathematical models of the epidemic dynamics of four compartments. We have collected data from the Djibouti health ministry. We study the positivity, boundedness, existence and uniqueness of the weak solution. Next, we define the Basic reproduction number by the method of the DFE and EEP. Then, we study the local and global stability and the bifurcation analysis of equilibrium to examine its epidemiological relevance. Finally, we analyze the fit of the data in comparison with the result of our mathematical results, to validate the model and estimate the important model parameters and prediction about the disease. We consider the real cases of Djibouti from 15th March to 15th May 2021.
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    Convergences and numerical analysis of a contact problem with normal compliance and unilateral constraint
    (African Journal of Mathematics and Computer Science Research, 2021-01-05) Souleiman, Yahyeh
    This paper represents a continuation of a previous study on “Analysis of a Sliding Frictional Contact Problem with Unilateral Constraint”. This study considers a mathematical model which describes the equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraints, associated to a sliding version of Coulomb’s law of dry friction. After a description of the model, the variational formulation was presented. Then, the dependence of the solution was studied with respect to the data and a convergence result was proven. Regularization method was also used to study the existence and uniqueness of the contact problem for which a convergence result was presented. Finally, a semidiscrete scheme was introduced for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, an optimal order error estimate was derived