Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
5 results
Search Results
Article Citation - WoS: 28Citation - Scopus: 32New Applications Related To Covid-19(Elsevier, 2021) Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Akgul, AliAnalysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.Article Citation - WoS: 17Citation - Scopus: 21Modeling the Transmission Dynamics of Delayed Pneumonia-Like Diseases With a Sensitivity of Parameters(Springer, 2021) Baleanu, Dumitru; Raza, Ali; Rafiq, Muhammad; Soori, Atif Hassan; Mohsin, Muhammad; Naveed, MuhammadPneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results.Article Citation - WoS: 20Citation - Scopus: 21Stability Analysis and Numerical Simulations of Spatiotemporal Hiv Cd4+t Cell Model With Drug Therapy(Amer inst Physics, 2020) Elsonbaty, Amr; Adel, Waleed; Baleanu, Dumitru; Rafiq, Muhammad; Ahmed, NaumanIn this study, an extended spatiotemporal model of a human immunodeficiency virus (HIV) CD4+ T cell with a drug therapy effect is proposed for the numerical investigation. The stability analysis of equilibrium points is carried out for temporal and spatiotemporal cases where stability regions in the space of parameters for each case are acquired. Three numerical techniques are used for the numerical simulations of the proposed HIV reaction-diffusion system. These techniques are the backward Euler, Crank-Nicolson, and a proposed structure preserving an implicit technique. The proposed numerical method sustains all the important characteristics of the proposed HIV model such as positivity of the solution and stability of equilibria, whereas the other two methods have failed to do so. We also prove that the proposed technique is positive, consistent, and Von Neumann stable. The effect of different values for the parameters is investigated through numerical simulations by using the proposed method. The stability of the proposed model of the HIV CD4+ T cell with the drug therapy effect is also analyzed.Article Citation - WoS: 28Citation - Scopus: 27Competitive Numerical Analysis for Stochastic Hiv/Aids Epidemic Model in a Two-Sex Population(inst Engineering Technology-iet, 2019) Rafiq, Muhammad; Baleanu, Dumitru; Shoaib Arif, Muhammad; Naveed, Muhammad; Ashraf, Kaleem; Raza, Ali; Arif, Muhammad ShoaibThis study is an attempt to explain a reliable numerical analysis of a stochastic HIV/AIDS model in a two-sex population considering counselling and antiretroviral therapy (ART). The authors are comparing the solutions of the stochastic and deterministic HIV/AIDS epidemic model. Here, an endeavour has been made to explain the stochastic HIV/AIDS epidemic model is comparatively more pragmatic in contrast with the deterministic HIV/AIDS epidemic model. The effect of threshold number H* holds on the stochastic HIV/AIDS epidemic model. If H* < 1 then condition helps us to control disease in a two-sex human population while H* > 1 explains the persistence of disease in the two-sex human population. Lamentably, numerical methods such as Euler-Maruyama, stochastic Euler, and stochastic Runge-Kutta do not work for large time step sizes. The recommended structure preserving framework of the stochastic non-standard finite difference (SNSFD) scheme conserve all vital characteristics such as positivity, boundedness, and dynamical consistency defined by Mickens. The effectiveness of counselling and ART may control HIV/AIDS in a two-sex population.Article Citation - WoS: 17Citation - Scopus: 19Competitive Analysis for Stochastic Influenza Model With Constant Vaccination Strategy(inst Engineering Technology-iet, 2019) Raza, Ali; Rafiq, Muhammad; Arif, Muhammad Shoaib; Ali, Muhammad Asghar; Baleanu, DumitruThis manuscript discusses a competitive analysis of stochastic influenza model with constant vaccination strategy. The stochastic influenza model is comparatively more pragmatic versus the deterministic influenza model. The effect of influenza generation number holds in the stochastic model. If the value of this number is less than one, this situation will help us to control the disease in a population. A greater than one value of this threshold number shows the persistence of disease to become endemic. The proposed structure for the stochastic influenza model as stochastic non-standard finite difference scheme conserve all vital characteristics like positivity, boundedness and dynamical consistency defined by Mickens.