A new study and modeling of COVID-19 disease through fractional models:A comparative paradigm  

作　　者：Muhammad Asad Ullah Nauman Raza 

机构地区：[1]Department of Mathematics,University of the Punjab,Lahore 54000,Pakistan

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2024年第4期674-699,共26页高校应用数学学报（英文版）（B辑）

摘　　要：In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.

关 键 词：Atangana-Baleanu fractional derivative Caputo fractional derivative Tou k-Atangana numeri-cal scheme Adams-Bashforth-Moulton predictor-corrector Reproduction number R_(0) 

分 类 号：O29[理学—应用数学] R181.3[理学—数学]