Journal of Mathematical Biology

, Volume 73, Issue 4, pp 919–946 | Cite as

Stochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapy

  • Daniel Sánchez-Taltavull
  • Arturo Vieiro
  • Tomás Alarcón
Article

Abstract

HIV-1 infected patients are effectively treated with highly active anti-retroviral therapy (HAART). Whilst HAART is successful in keeping the disease at bay with average levels of viral load well below the detection threshold of standard clinical assays, it fails to completely eradicate the infection, which persists due to the emergence of a latent reservoir with a half-life time of years and is immune to HAART. This implies that life-long administration of HAART is, at the moment, necessary for HIV-1-infected patients, which is prone to drug resistance and cumulative side effects as well as imposing a considerable financial burden on developing countries, those more afflicted by HIV, and public health systems. The development of therapies which specifically aim at the removal of this latent reservoir has become a focus of much research. A proposal for such therapy consists of elevating the rate of activation of the latently infected cells: by transferring cells from the latently infected reservoir to the active infected compartment, more cells are exposed to the anti-retroviral drugs thus increasing their effectiveness. In this paper, we present a stochastic model of the dynamics of the HIV-1 infection and study the effect of the rate of latently infected cell activation on the average extinction time of the infection. By analysing the model by means of an asymptotic approximation using the semi-classical quasi steady state approximation (QSS), we ascertain that this therapy reduces the average life-time of the infection by many orders of magnitudes. We test the accuracy of our asymptotic results by means of direct simulation of the stochastic process using a hybrid multi-scale Monte Carlo scheme.

Keywords

HIV-1 HAART Latently infection Stochastic modelling Antigen stimulation 

Mathematics Subject Classification

34E20 Singular perturbations turning point theory WKB methods 34E13 Multiple scale methods 92B05 General biology and biomathematics 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Daniel Sánchez-Taltavull
    • 1
    • 4
  • Arturo Vieiro
    • 2
  • Tomás Alarcón
    • 3
    • 4
    • 5
    • 6
  1. 1.Regenerative Medicine ProgramOttawa Hospital Research InstituteOttawaCanada
  2. 2.Departament de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain
  3. 3.ICREA (Institució Catalana de Recerca i Estudis Avançats)BarcelonaSpain
  4. 4.Centre de Recerca Matemàtica, Edifici CBarcelonaSpain
  5. 5.Departament de MatemàtiquesUniversitat Autònoma de Barcelona, BellaterraBarcelonaSpain
  6. 6.Barcelona Graduate School of Mathematics (BGSMath)BarcelonaSpain

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