Yazar "Yasin, Muhammad W." seçeneğine göre listele

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    Computational aspects of an epidemic model involving stochastic partial differential equations
    (World Scientific Publ Co Pte Ltd, 2023) Ahmed, Nauman; Yasin, Muhammad W.; Ali, Syed Mansoor; Akguel, Ali; Raza, Ali; Rafiq, Muhammad; Shar, Muhammad Ali
    This paper deals with the study of the reaction-diffusion epidemic model perturbed with time noise. It has various applications such as disease in population models of humans, wildlife, and many others. The stochastic SIR model is numerically investigated with the proposed stochastic backward Euler scheme and proposed stochastic implicit finite difference (IFD) scheme. The stability of the proposed methods is shown with Von Neumann criteria and both schemes are unconditionally stable. Both schemes are consistent with systems of the equations in the mean square sense. The numerical solution obtained by the proposed stochastic backward Euler scheme and solutions converges towards an equilibrium but it has negative and divergent behavior for some values. The numerical solution gained by the proposed IFD scheme preserves the positivity and also solutions converge towards endemic and disease-free equilibrium. We have used two problems to check our findings. The graphical behavior of the stochastic SIR model is much adjacent to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The results show the efficacy of the proposed stochastic IFD scheme.
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    Investigating the impact of stochasticity on HIV infection dynamics in CD4+T cells using a reaction-diffusion model
    (Nature Portfolio, 2024) Ahmed, Nauman; Yasin, Muhammad W.; Ali, Syed Mansoor; Akgul, Ali; Raza, Ali; Rafiq, Muhammad; Muhammad, Shah
    The disease dynamics affect the human life. When one person is affected with a disease and if it is not treated well, it can weaken the immune system of the body. Human Immunodeficiency Virus (HIV) is a virus that attacks the immune system, of the body which is the defense line against diseases. If it is not treated well then HIV progresses to its advanced stages and it is known as Acquired Immunodeficiency Syndrome (AIDS). HIV is typically a disease that can transferred from one person to another in several ways such as through blood, breastfeeding, sharing needles or syringes, and many others. So, the need of the hour is to consider such important disease dynamics and that will help mankind to save them from such severe disease. For the said purpose the reaction-diffusion HIV CD4+ T cell model with drug therapy under the stochastic environment is considered. The underlying model is numerically investigated with two time-efficient schemes and the effects of various parameters used in the model are analyzed and explained in a real-life scenario. Additionally, the obtained results will help the decision-makers to avoid such diseases. The random version of the HIV model is numerically investigated under the influence of time noise in Ito<^> sense. The proposed stochastic backward Euler (SBE) scheme and proposed stochastic Implicit finite difference (SIFD) scheme are developed for the computational study of the underlying model. The consistency of the schemes is proven in the mean square sense and the given system of equations is compatible with both schemes. The stability analysis proves that both schemes and schemes are unconditionally stable. The given system of equations has two equilibria, one is disease-free equilibrium (DFE) and the other is endemic equilibrium. The simulations are drawn for the different values of the parameters. The proposed SBE scheme showed the convergent behavior towards the equilibria for the given values of the parameters but also showed negative behavior that is not biological. The proposed SIFD scheme showed better results as compared with the stochastic SBE scheme. This scheme has convergent and positive behavior towards the equilibria points for the given values of the parameters. The effect of various parameters is also analyzed. Simulations are drawn to evaluate the efficacy of the schemes.
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    Numerical scheme and stability analysis of stochastic Fitzhugh-Nagumo model
    (Elsevier, 2022) Yasin, Muhammad W.; Iqbal, Muhammad S.; Ahmed, Nauman; Akgul, Ali; Raza, Ali; Rafiq, Muhammad; Riaz, Muhammad Bilal
    This article deals with the Fitzhugh-Nagumo equation in the presence of stochastic function. A numerical scheme has been developed for the solution of such equations which preserves the certain structure of the unknown functions, also we have given the stability analysis, consistency of the problem, and explicitly optimal a priori estimates for the existence of solutions of such equations. A unique solution has been guaranteed. The corresponding explicit estimates in the function spaces are formulated in the form of theorems. Lastly, one important feature of the article is the simulation of the proposed numerical scheme in the form of the 2D and 3D plots which shows the efficacy of the stochastic analysis of such nonlinear partial differential equations.
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    Reliable numerical analysis for stochastic reaction-diffusion system
    (Iop Publishing Ltd, 2023) Yasin, Muhammad W.; Ahmed, Nauman; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Raza, Ali; Akgul, Ali
    In this article, stochastic behavior of reaction diffusion brusselator model is under consideration. There are many physical phenomena which are related to chemical concentrations. One chemical concentration coincide with the other chemical concentration and their inter-diffusion is a major question to be addressed and to be understood. So, that is why Brusselator model is very proto-type and standard model that lays the foundation of any kind of that matter chemical concentrations of different substances. It also has the application in physical species as well. That is why we are considering such model. The existence of solution is guaranteed with fix-point operator, self mapping and pre-compact conditions. Nonstandard finite difference scheme and Crank-Nicolson schemes are used to show the graphical behavior of the model. The consistency and stability of the schemes are discussed and both schemes are unconditionally stable. The 3D and 2D graphs represents the concentration of the models.