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The role of synaptic transmission in a HIV model with memory

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  • Pinto, Carla M.A.
  • Carvalho, Ana R.M.

Abstract

We propose a mathematical model with memory for the dynamics of HIV epidemics, where two transmission modes, cell-to-cell and virus-to-cell, and drug resistance are considered. Systems with memory, or fractional order systems, have largely been applied to the modeling of several real life phenomena. Here, we consider a fractional model where the order of the non-integer derivative takes values in the interval [0.5, 1.0]. We prove the local and global stability of the disease-free equilibrium. We study the role of the cell-to-cell transmission probability on the dynamics of the model, and on the value of the reproduction number, R0, for distinct values of the fractional order derivative, α. Moreover, we show evidence of an improvement of HIV infected patients quality of life, due to the increase of the drug efficacy. In the end, important inferences are drawn.

Suggested Citation

  • Pinto, Carla M.A. & Carvalho, Ana R.M., 2017. "The role of synaptic transmission in a HIV model with memory," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 76-95.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:76-95
    DOI: 10.1016/j.amc.2016.07.031
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    References listed on IDEAS

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    1. Alex Sigal & Jocelyn T. Kim & Alejandro B. Balazs & Erez Dekel & Avi Mayo & Ron Milo & David Baltimore, 2011. "Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy," Nature, Nature, vol. 477(7362), pages 95-98, September.
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    Cited by:

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    2. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    3. Zafar, Zain Ul Abadin & Ali, Nigar & Baleanu, Dumitru, 2021. "Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    5. Wang, Mei & Du, Feifei & Chen, Churong & Jia, Baoguo, 2019. "Asymptotic stability of (q, h)-fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 158-167.
    6. Thirumalai, Sagithya & Seshadri, Rajeswari & Yuzbasi, Suayip, 2021. "Spectral solutions of fractional differential equations modelling combined drug therapy for HIV infection," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    7. Shi, Ruiqing & Lu, Ting & Wang, Cuihong, 2021. "Dynamic analysis of a fractional-order model for HIV with drug-resistance and CTL immune response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 509-536.
    8. Huang, Lan-Lan & Baleanu, Dumitru & Mo, Zhi-Wen & Wu, Guo-Cheng, 2018. "Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 166-175.

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