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

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  • Naik, Parvaiz Ahmad
  • Zu, Jian
  • Owolabi, Kolade M.

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-Bashforth-Moulton 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.

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  • Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920302265
    DOI: 10.1016/j.chaos.2020.109826
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    References listed on IDEAS

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    10. Kar, Silajit & Maiti, Dilip K. & Maiti, Atasi Patra, 2024. "Impacts of non-locality and memory kernel of fractional derivative, awareness and treatment strategies on HIV/AIDS prevalence," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    11. Samad Noeiaghdam & Denis Sidorov & Alyona Zamyshlyaeva & Aleksandr Tynda & Aliona Dreglea, 2020. "A Valid Dynamical Control on the Reverse Osmosis System Using the CESTAC Method," Mathematics, MDPI, vol. 9(1), pages 1-17, December.
    12. Alzahrani, Faris & Razzaq, Oyoon Abdul & Rehman, Daniyal Ur & Khan, Najeeb Alam & Alshomrani, Ali Saleh & Ullah, Malik Zaka, 2022. "Repercussions of unreported populace on disease dynamics and its optimal control through system of fractional order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    13. Samad Noeiaghdam & Aliona Dreglea & Hüseyin Işık & Muhammad Suleman, 2021. "A Comparative Study between Discrete Stochastic Arithmetic and Floating-Point Arithmetic to Validate the Results of Fractional Order Model of Malaria Infection," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
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    More about this item

    Keywords

    SEIR epidemic model; Caputo fractional derivative; Adams-Bashforth-Moulton method; Female sex workers; Stability analysis; Reproduction number R0; Fractional optimal control problem;
    All these keywords.

    JEL classification:

    • R0 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General

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