Browsing by Author "Shehzad, Aamir"

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Citation - WoS: 20
Citation - Scopus: 25
Analysis of a fractional order Bovine Brucellosis disease model with discrete generalized Mittag–Leffler kernels
(Elsevier, 2023) Farman, Muhammad; Baleanu, Dumitru; Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; Attia, Nourhane; Hassan, Ahmed M.; 56389; Matematik
Bovine Brucellosis, a zoonotic disease, can infect cattle in tropical and subtropical areas. It remains a critical issue for both human and animal health in many parts of the world, especially those where livestock is an important source of food and income. An efficient method for monitoring the illness's increasing prevalence and developing low-cost prevention strategies for both its effects and recurrence is brucellosis disease modeling. We create a fractional-order model of Bovine Brucellosis using a discrete modified Atangana-Baleanu fractional difference operator of the Liouville-Caputo type. An analysis of the suggested system's well-posedness and a qualitative investigation are both conducted. The examination of the Volterra-type Lyapunov function for global stability is supported by the first and derivative tests. The Lipschitz condition is also used for the model in order to meet the criterion of the uniqueness of the exact solution. We created an endemic and disease-free equilibrium. Solutions are built in the discrete generalized form of the Mittag-Leffler kernel in order to analyze the effect of the fractional operator with numerical simulations and emphasize the effects of the sickness due to the many factors involved. The capacity of the suggested model to forecast an infectious disease like brucellosis can help researchers and decision-makers take preventive actions.
Citation - WoS: 47
Citation - Scopus: 54
Modelling and Analysis of a Measles Epidemic Model with the Constant Proportional Caputo Operator
(Mdpi, 2023) Farman, Muhammad; Baleanu, Dumitru; Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; De la Sen, Manuel; 56389; Matematik
Despite the existence of a secure and reliable immunization, measles, also known as rubeola, continues to be a leading cause of fatalities globally, especially in underdeveloped nations. For investigation and observation of the dynamical transmission of the disease with the influence of vaccination, we proposed a novel fractional order measles model with a constant proportional (CP) Caputo operator. We analysed the proposed model's positivity, boundedness, well-posedness, and biological viability. Reproductive and strength numbers were also verified to examine how the illness dynamically behaves in society. For local and global stability analysis, we introduced the Lyapunov function with first and second derivatives. In order to evaluate the fractional integral operator, we used different techniques to invert the PC and CPC operators. We also used our suggested model's fractional differential equations to derive the eigenfunctions of the CPC operator. There is a detailed discussion of additional analysis on the CPC and Hilfer generalised proportional operators. Employing the Laplace with the Adomian decomposition technique, we simulated a system of fractional differential equations numerically. Finally, numerical results and simulations were derived with the proposed measles model. The intricate and vital study of systems with symmetry is one of the many applications of contemporary fractional mathematical control. A strong tool that makes it possible to create numerical answers to a given fractional differential equation methodically is symmetry analysis. It is discovered that the proposed fractional order model provides a more realistic way of understanding the dynamics of a measles epidemic.