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Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative

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  • Yusuf, Abdullahi
  • Tasiu Mustapha, Umar
  • Abdulkadir Sulaiman, Tukur
  • Hincal, Evren
  • Bayram, Mustafa

Abstract

In this research, we propose a deterministic model to study the transmission dynamics of HIV infection in the Caputo fractional operator context and analyze the impact of horizontal and vertical transmissions of the infection. The model consisting of mutually exclusive compartments representing the human dynamics, has a locally-asymptotically stable disease free equilibrium (DFE) whenever a certain epidemiological threshold quantity known as the basic reproduction number R0 is less-than unity. Significant model characteristics such as the existence and uniqueness of the solution and sensitivity analysis are investigated. Finally, In order to evaluate the approximate solution and dynamical behavior of the model under consideration, the well-known and efficient numerical scheme called the fractional Euler method is employed and the results show that, the infections from the compartments of each state variables decreases with time which causes an increase in the compartments of new born child with no HIV infection and susceptible adults. It should be noted that, unlike many studies recently carried out, dimensional consistency is taken into account during the classical model fractionalization process.

Suggested Citation

  • Yusuf, Abdullahi & Tasiu Mustapha, Umar & Abdulkadir Sulaiman, Tukur & Hincal, Evren & Bayram, Mustafa, 2021. "Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001466
    DOI: 10.1016/j.chaos.2021.110794
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    References listed on IDEAS

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    1. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
    2. Qureshi, Sania, 2020. "Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 151-165.
    3. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    4. Mustapha, Umar Tasiu & Hincal, Evren, 2020. "An optimal control of hookworm transmissions model with differential infectivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    5. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    6. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    7. Din, Anwarud & Khan, Amir & Baleanu, Dumitru, 2020. "Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    9. Mustapha, Umar Tasiu & Qureshi, Sania & Yusuf, Abdullahi & Hincal, Evren, 2020. "Fractional modeling for the spread of Hookworm infection under Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    10. Rosa, Silvério & Torres, Delfim F.M., 2018. "Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 142-149.
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    Cited by:

    1. 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).

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