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        Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control

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        0960-0779
        https://doi.org/10.1016/j.chaos.2020.109826
        http://hdl.handle.net/20.500.12010/12091
        https://doi.org/10.1016/j.chaos.2020.109826
        http://repositorioslatinoamericanos.uchile.cl/handle/2250/3509273
        Author
        Ahmad Naik, Parvaiz
        Zu, Jian
        Owolabi, Kolade M.
        Institutions
        • Universidad Jorge Tadeo Lozano (Colombia)
        Abstract
        In this paper, a nonlinear fractional order epidemic model for HIV transmission is proposed and analyzed by including extra compartment namely exposed class to the basic SIR epidemic model. Also, the infected class of female sex workers is divided into unaware infectives and the aware infectives. The focus is on the spread of HIV by female sex workers through prostitution, because in the present world sexual transmission is the major cause of the HIV transmission. The exposed class contains those susceptible males in the population who have sexual contact with the female sex workers and are exposed to the infection directly or indirectly. The Caputo type fractional derivative is involved and generalized Adams-BashforthMoulton method is employed to numerically solve the proposed model. Model equilibria are determined and their stability analysis is considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle invariant principle. Analysis of the model demonstrates that the population is free from the disease if R0 < 1 and disease spreads in the population if R0 > 1. Meanwhile, by using Lyapunov functional approach, the global dynamics of the endemic equilibrium point is discussed. Furthermore, for the fractional optimal control problem associated with the control strategies such as condom use for exposed class, treatment for aware infectives, awareness about disease among unaware infectives and behavioral change for susceptibles, we formulated a fractional optimality condition for the proposed model. The existence of fractional optimal control is analyzed and the Euler-Lagrange necessary conditions for the optimality of fractional optimal control are obtained. The effectiveness of control strategies is shown through numerical simulations and it can be seen through simulation, that the control measures effectively increase the quality of life and age limit of the HIV patients. It significantly reduces the number of HIV/AIDS patients during the whole epidemic.
        Subjects
        SEIR epidemic model
        Caputo fractional derivative
        Adams-Bashforth-Moulton method
        Female sex workers
        Stability analysis
        Reproduction number R0
        Fractional optimal control problem

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        Red de Repositorios Latinoamericanos
        + of 4.000.000
        Available publications
        163 Participating institutions
        Dirección de Servicios de Información y Bibliotecas (SISIB)
        Universidad de Chile
        Membership Login
        Featured collections
        • Latin American Theses
        • Argentinean Theses
        • Chilean Theses
        • Peruvian Theses
        Latest collections added
        • Argentina
        • Brazil
        • Colombia
        • México
        Dirección de Servicios de Información y Bibliotecas (SISIB)
        Universidad de Chile
        Red de Repositorios Latinoamericanos | 2006-2018