Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 3Citation - Scopus: 6Mathematical and Numerical Investigations of the Fractional-Order Epidemic Model With Constant Vaccination Strategy(Editura Acad Romane, 2021) Iqbal, Zafar; Baleanu, Dumitru; Rehman, Muhammad Aziz Ur; Baleanu, Dumitru; Ahmed, Nauman; Raza, Ali; Rafiq, Muhammad; MatematikThis work is devoted to find the reliable numerical solution of an epidemic model with constant vaccination strategy. For this purpose, a structure preserving numerical scheme called the Grunwald-Letnikov nonstandard finite difference scheme is designed. The proposed technique retains all the important properties of the continuous epidemic model like boundedness, positivity, and stability. This behavior of the proposed numerical scheme is validated mathematically and graphically. The role of the vaccination in controlling the disease dynamics in the population is verified through numerical simulations. The stability of the system under discussion is also examined at the disease free equilibrium point and the endemic equilibrium point. Finally, the outcome of this study is furnished with concluding remarks and future directions of research.Article Citation - WoS: 4Citation - Scopus: 3Analysis and Numerical Effects of Time-Delayed Rabies Epidemic Model With Diffusion(Walter de Gruyter Gmbh, 2023) Rehman, Muhammad Aziz-Ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Raza, Ali; Jawaz, MuhammadThe current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von-Neumann method. Taylor's expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of tau on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.