Browsing by Author "Raza, N."

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Fractional Dynamics and Sensitivity Analysis of Measles Epidemic Model Through Vaccination
(Taylor and Francis Ltd., 2024) Riaz, M.B.; Raza, N.; Martinovic, J.; Bakar, A.; Kurkcu, H.; Tunç, O.
Measles is a highly contagious disease that mainly affects children worldwide. Even though a reliable and effective vaccination is available, there were 140,000 measles deaths worldwide in 2018, and most of them were children under the age five years. In this paper, we comprehensively investigate a novel fractional SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) model of the measles epidemic powered by nonlinear fractional differential equations to understand the epidemic’s dynamical behaviour. We use a non-singular Atangana-Baleanu fractional derivative to analyze the proposed model, taking advantage of non-locality. The existence, uniqueness, positivity and boundedness of the solutions are shown via concepts of fixed point theory, and we also perform the Ulam-Hyers stability of the considered model. The parameter sensitivity is discussed in the context of the variance with each parameter using 3-D graphics based on the basic reproduction number. Moreover, with the Atangana-Toufik numerical scheme, numerical findings are depicted for different fractional-order values. The presented approach produce results that are efficiently consistent and in excellent agreement with the theoretical results. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
Numerical Simulations of the Fractional-Order Siq Mathematical Model of Corona Virus Disease Using the Nonstandard Finite Difference Scheme
(Univ Putra Malaysia Press, 2022) Raza, N.; Bakar, A.; Khan, A.; Tunc, C.
This paper proposes a novel nonlinear fractional-order pandemic model with Caputo derivative for corona virus disease. A nonstandard finite difference (NSFD) approach is presented to solve this model numerically. This strategy preserves some of the most significant physical properties of the solution such as non-negativity, boundedness and stability or convergence to a stable steady state. The equilibrium points of the model are analyzed and it is determined that the proposed fractional model is locally asymptotically stable at these points. Non-negativity and boundedness of the solution are proved for the considered model. Fixed point theory is employed for the existence and uniqueness of the solution. The basic reproduction number is computed to investigate the dynamics of corona virus disease. It is worth mentioning that the non-integer derivative gives significantly more insight into the dynamic complexity of the corona model. The suggested technique produces dynamically consistent outcomes and excellently matches the analyticalworks. To illustrate our results, we conduct a comprehensive quantitative study of the proposed model at various quarantine levels. Numerical simulations show that can eradicate a pandemic quickly if a human population implements obligatory quarantine measures at varying coverage levels while maintaining sufficient knowledge.