Browsing by Author "Obaid, Hasim"

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    An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection
    (De Gruyter Open, 2013) Obaid, Hasim; Ouifki, Rachid; Patidar, Kailash C.
    We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.
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    Optimal control strategies applied to a mathematical model of meningitis
    (New York Business Global, 2025) Patidar, Kailash; Mohamed, Sahar; Obaid, Hasim
    In this paper, we deal with the problem of optimal control for the transmission dynamics of the meningococcal meningitis. The problem is a mathematical model described by a system of nonlinear differential equations. Based on this, two controls are formulated and the resulting system is solved as an optimal control problem. Aiming to minimize the number of illnesses or deaths in the population, we used a control representing a vaccination and another one representing a treatment strategy. We prove that these controls are capable of reducing the number of carriers and infectious individuals. Numerical simulations are carried out to show how to perform the two strategies.