title: Stochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapy.
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.
authors.affiliation: Regenerative Medicine Program, Ottawa Hospital Research Institute, Ottawa, K1H 8L6, Canada. dsanchez@crm.cat.|Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, Bellaterra, 08193, Barcelona, Spain. dsanchez@crm.cat.
authors.forename: Daniel
authors.initials: D
authors.lastname: Sánchez-Taltavull
authors.affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08007, Barcelona, Spain.
authors.forename: Arturo
authors.initials: A
authors.lastname: Vieiro
authors.affiliation: ICREA (Institució Catalana de Recerca i Estudis Avançats), Barcelona, Spain.|Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, Bellaterra, 08193, Barcelona, Spain.|Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Spain.|Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain.
authors.forename: Tomás
authors.initials: T
authors.lastname: Alarcón
mesh_terms: D044966:Anti-Retroviral Agents / Q000627:therapeutic use*; D023241:Antiretroviral Therapy, Highly Active / Q000706:statistics & numerical data*; D060740:Disease Eradication; D015658:HIV Infections / Q000188:drug therapy*; D015497:HIV-1; D006207:Half-Life; D006801:Humans; D008954:Models, Biological; D019562:Viral Load; D017735:Virus Latency
chemical_list: D044966:Anti-Retroviral Agents
keywords: Antigen stimulation; HAART; HIV-1; Latently infection; Stochastic modelling