Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 4Citation - Scopus: 3Evolutionary Computational Method for Tuberculosis Model With Fuzziness(Aip Publishing, 2023) Dayan, Fazal; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Raza, Ali; Alsaadi, AteqThis work investigates the computational study of a six-compartmental mathematical model of tuberculosis disease dynamics with the impact of vaccination. Traditional mathematical models presume that all variables are precise and can be measured or calculated precisely. However, in many real-world scenarios, variables may need to be more accurate or easier to quantify, resulting in model uncertainty. Considering this, fuzziness is introduced into the model by taking the contact, recovery, and death rates due to disease as fuzzy membership functions. Two numerical computational schemes, forward Euler and nonstandard finite difference (NSFD), are designed to solve the model. The positivity and convergence for the developed method are investigated, which are significant characteristics of these dynamical models, and it is revealed that these features are preserved in the extended scheme. Numerical computations are performed to support the analytical results. The numerical and computational results indicate that the proposed NSFD method adequately represents the dynamics of the disease despite the uncertainty and heterogeneity. Moreover, the obtained method generates plausible predictions that regulators can use to design and develop control strategies to support decision-making.Article Citation - WoS: 6Citation - Scopus: 6Dynamical Analysis of a Class of Seir Models Through Delayed Strategies(Aip Publishing, 2023) Rafiq, Muhammad; Ahmed, Nauman; Baleanu, Dumitru; Alfwzan, Wafa F.; Raza, AliIn recent decades, the mathematical modeling of infectious diseases, real-world problems, non-linear dynamical complex systems, etc., has increased significantly. According to World Health Organization, tobacco use is the cause of about 22% of cancer deaths. Another 10% are due to obesity, poor diet, lack of physical activity, and excessive drinking of alcohol. Approximately 5%-10% of cancers are due to inherited genetic defects. The objective is to investigate the impact of time delays in implementing control measures on the epidemic dynamics. The classification of cell population has four compartments: susceptible cells (x), cancer-infected cells (y), virus-free cells (v), and immune cells (z). Our focus is to find the equilibria of the problem and their stability. The stability of the solutions is of two types: locally asymptotic and globally asymptotic. The Routh-Hurwitz criterion, Volterra-type Lyapunov function, and LaSalle's invariance principle are used to verify the stability of solutions. The graphical behavior depicts the stable solutions to a real-world problem and supports the stability analysis of the problem. The findings contribute to the understanding of epidemic dynamics and provide valuable information for designing and implementing effective intervention strategies in public health systems.Article Citation - WoS: 30Citation - Scopus: 32Spatio-Temporal Numerical Modeling of Reaction-Diffusion Measles Epidemic System(Aip Publishing, 2019) Wei, Zhouchao; Baleanu, Dumitru; Rafiq, M.; Rehman, M. A.; Ahmed, NaumanIn this work, we investigate the numerical solution of the susceptible exposed infected and recovered measles epidemic model. We also evaluate the numerical stability and the bifurcation value of the transmission parameter from susceptibility to a disease of the proposed epidemic model. The proposed method is a chaos free finite difference scheme, which also preserves the positivity of the solution of the given epidemic model. Published under license by AIP Publishing.