Bulletin of Mathematical Biology

, Volume 81, Issue 1, pp 131–154 | Cite as

Stochastic Dynamics of the Latently Infected Cell Reservoir During HIV Infection

  • Shaimaa A. Azoz
  • Daniel Coombs
Original Article


The presence of cells latently infected with HIV is currently considered to be a major barrier to viral eradication within a patient. Here, we consider birth–death-immigration models for the latent cell population in a single patient, and present analytical results for the size of this population in the absence of treatment. We provide results both at steady state (viral set point), and during the non-equilibrium setting of early infection. We obtain semi-analytic results showing how latency-reversing drugs might be expected to affect the size of the latent pool over time. We also analyze the probability of rare mutant viral strains joining the latent cell population, allowing for steady-state and dynamic viral populations within the host.


HIV Virus dynamics Latently infected cells Antiretroviral therapy Latency-reducing therapy 



We thank Jessica M. Conway and Alejandra D. Herrera for helpful discussions and references.


  1. Alexander HK, Bonhoeffer S (2012) Pre-existence and emergence of drug resistance in a generalized model of intra-host viral dynamics. Epidemics 4(4):187–202. CrossRefGoogle Scholar
  2. Allen L (2010) An introduction to stochastic processes with applications to biology, 2nd edn. Chapman and Hall, Upper Saddle RiverGoogle Scholar
  3. Althaus CL, Joos B, Perelson AS, Günthard HF (2014) Quantifying the turnover of transcriptional subclasses of HIV-1-infected cells. PLoS Comput Biol 10(10):e1003,871. CrossRefGoogle Scholar
  4. Archin NM, Liberty AL, Kashuba AD, Choudhary SK, Kuruc JD, Crooks AM, Parker DC, Anderson EM, Kearney MF, Strain MC, Richman DD, Hudgens MG, Bosch RJ, Coffin JM, Eron JJ, Hazuda DJ, Margolis DM (2012) Administration of vorinostat disrupts HIV-1 latency in patients on antiretroviral therapy. Nature 487(7408):482–5. CrossRefGoogle Scholar
  5. Archin NM, Sung JM, Garrido C, Soriano-Sarabia N, Margolis DM (2014) Eradicating HIV-1 infection: seeking to clear a persistent pathogen. Nat Rev Microbiol 12(11):750–64. CrossRefGoogle Scholar
  6. Bonhoeffer S, Nowak MA (1997) Pre-existence and emergence of drug resistance in HIV-1 infection. Proc Biol Sci 264(1382):631–7. CrossRefGoogle Scholar
  7. Bullen CK, Laird GM, Durand CM, Siliciano JD, Siliciano RF (2014) New ex vivo approaches distinguish effective and ineffective single agents for reversing HIV-1 latency in vivo. Nat Med 20(4):425–9. CrossRefGoogle Scholar
  8. Chomont N, El-Far M, Ancuta P, Trautmann L, Procopio FA, Yassine-Diab B, Boucher G, Boulassel MR, Ghattas G, Brenchley JM, Schacker TW, Hill BJ, Douek DC, Routy JP, Haddad EK, Sékaly RP (2009) HIV reservoir size and persistence are driven by T cell survival and homeostatic proliferation. Nat Med 15(8):893–900. CrossRefGoogle Scholar
  9. Chun TW, Engel D, Mizell SB, Ehler LA, Fauci AS (1998) Induction of HIV-1 replication in latently infected CD4+ T cells using a combination of cytokines. J Exp Med 188(1):83–91CrossRefGoogle Scholar
  10. Conway JM, Coombs D (2011) A stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients. PLoS Comput Biol 7(4):e1002033. MathSciNetCrossRefGoogle Scholar
  11. Conway JM, Perelson AS (2015) Post-treatment control of HIV infection. Proc Natl Acad Sci USA 112(17):5467–5472. CrossRefGoogle Scholar
  12. Conway JM, Konrad BP, Coombs D (2013) Stochastic analysis of pre- and postexposure prophylaxis against HIV infection. SIAM J. Appl. Math. 73(2):904–928. MathSciNetCrossRefzbMATHGoogle Scholar
  13. Elliott JH, McMahon JH, Chang CC, Lee SA, Hartogensis W, Bumpus N, Savic R, Roney J, Hoh R, Solomon A, Piatak M, Gorelick RJ, Lifson J, Bacchetti P, Deeks SG, Lewin SR (2015) Short-term administration of disulfiram for reversal of latent HIV infection: a phase 2 dose-escalation study. Lancet HIV 2(12):e520–9. CrossRefGoogle Scholar
  14. Finzi D, Blankson J, Siliciano JD, Margolick JB, Chadwick K, Pierson T, Smith K, Lisziewicz J, Lori F, Flexner C, Quinn TC, Chaisson RE, Rosenberg E, Walker B, Gange S, Gallant J, Siliciano RF (1999) Latent infection of CD4+ T cells provides a mechanism for lifelong persistence of HIV-1, even in patients on effective combination therapy. Nat Med 5(5):512–7. CrossRefGoogle Scholar
  15. Gadhamsetty S, Dixit NM (2010) Estimating frequencies of minority nevirapine-resistant strains in chronically HIV-1-infected individuals naive to nevirapine by using stochastic simulations and a mathematical model. J Virol 84(19):10,230–40. CrossRefGoogle Scholar
  16. Gutiérrez C, Serrano-Villar S, Madrid-Elena N, Pérez-Elías MJ, Martín ME, Barbas C, Ruipérez J, Muñoz E, Muñoz-Fernández MA, Castor T, Moreno S (2016) Bryostatin-1 for latent virus reactivation in HIV-infected patients on antiretroviral therapy. AIDS 30(9):1385–92. CrossRefGoogle Scholar
  17. Hill AL, Rosenbloom DIS, Fu F, Nowak MA, Siliciano RF (2014) Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1. Proc Natl Acad Sci USA 111(37):13475–13480. CrossRefGoogle Scholar
  18. Hill AL, Rosenbloom DIS, Goldstein E, Hanhauser E, Kuritzkes DR, Siliciano RF, Henrich TJ (2016a) Real-time predictions of reservoir size and rebound time during antiretroviral therapy interruption trials for HIV. PLoS Pathog 12(4):e1005,535. CrossRefGoogle Scholar
  19. Hill AL, Rosenbloom DIS, Siliciano JD, Siliciano RF (2016b) Insufficient evidence for rare activation of latent HIV in the absence of reservoir-reducing interventions. PLoS Pathog 12(8):e1005,679. CrossRefGoogle Scholar
  20. Ho YC, Shan L, Hosmane NN, Wang J, Laskey SB, Rosenbloom DIS, Lai J, Blankson JN, Siliciano JD, Siliciano RF (2013) Replication-competent noninduced proviruses in the latent reservoir increase barrier to HIV-1 cure. Cell 155(3):540–51. CrossRefGoogle Scholar
  21. Hosmane NN, Kwon KJ, Bruner KM, Capoferri AA, Beg S, Rosenbloom DIS, Keele BF, Ho YC, Siliciano JD, Siliciano RF (2017) Proliferation of latently infected CD4+ T cells carrying replication-competent HIV-1: Potential role in latent reservoir dynamics. J Exp Med 214(4):959–972. CrossRefGoogle Scholar
  22. Joos B, Fischer M, Kuster H, Pillai SK, Wong JK, Böni J, Hirschel B, Weber R, Trkola A, Günthard HF, Swiss HIV Cohort Study (2008) HIV rebounds from latently infected cells, rather than from continuing low-level replication. Proc Natl Acad Sci USA 105(43):16,725–30, DOIurl10.1073/pnas.0804192105Google Scholar
  23. Karlin S, Taylor H (1974) A first course in stochastic processes, 2nd edn. Academic Press Inc, LondonzbMATHGoogle Scholar
  24. Kendall D (1957) On the generalized birth-and-death process. Ann Math Stat 19:1–15MathSciNetCrossRefzbMATHGoogle Scholar
  25. Kim H, Perelson AS (2006) Viral and latent reservoir persistence in HIV-1-infected patients on therapy. PLoS Comput Biol 2(10):e135. CrossRefGoogle Scholar
  26. Konrad BP, Taylor D, Conway JM, Ogilvie GS, Coombs D (2017) On the duration of the period between exposure to HIV and detectable infection. Epidemics 20:73–83. CrossRefGoogle Scholar
  27. Margolis DM, Garcia JV, Hazuda DJ, Haynes BF (2016) Latency reversal and viral clearance to cure HIV-1. Science 353(6297):aaf6517,
  28. Monie D, Simmons RP, Nettles RE, Kieffer TL, Zhou Y, Zhang H, Karmon S, Ingersoll R, Chadwick K, Zhang H, Margolick JB, Quinn TC, Ray SC, Wind-Rotolo M, Miller M, Persaud D, Siliciano RF (2005) A novel assay allows genotyping of the latent reservoir for human immunodeficiency virus type 1 in the resting CD4+ T cells of viremic patients. J Virol 79(8):5185–202. CrossRefGoogle Scholar
  29. Müller V, Vigueras-Gómez JF, Bonhoeffer S (2002) Decelerating decay of latently infected cells during prolonged therapy for human immunodeficiency virus type 1 infection. J Virol 76(17):8963–5CrossRefGoogle Scholar
  30. Perelson A, Nelson P (1999) Mathematical models of HIV-1 dynamics in vivo. SIAM Rev 41:3–44MathSciNetCrossRefzbMATHGoogle Scholar
  31. Perelson AS, Essunger P, Cao Y, Vesanen M, Hurley A, Saksela K, Markowitz M, Ho DD (1997) Decay characteristics of HIV-1-infected compartments during combination therapy. Nature 387(6629):188–91. CrossRefGoogle Scholar
  32. Pinkevych M, Cromer D, Tolstrup M, Grimm AJ, Cooper DA, Lewin SR, Søgaard OS, Rasmussen TA, Kent SJ, Kelleher AD, Davenport MP (2015) HIV reactivation from latency after treatment interruption occurs on average every 5-8 days–implications for HIV remission. PLoS Pathog 11(7):e1005,000. CrossRefGoogle Scholar
  33. Rasmussen TA, Tolstrup M, Søgaard OS (2016) Reversal of latency as part of a cure for HIV-1. Trends Microbiol 24(2):90–97. CrossRefGoogle Scholar
  34. Renshaw E (2011) Stochastic population processes: analysis, approximations, simulations. Oxford University Press, OxfordCrossRefzbMATHGoogle Scholar
  35. Ribeiro RM, Bonhoeffer S (2000) Production of resistant HIV mutants during antiretroviral therapy. Proc Natl Acad Sci USA 97(14):7681–6CrossRefzbMATHGoogle Scholar
  36. Ribeiro RM, Bonhoeffer S, Nowak MA (1998) The frequency of resistant mutant virus before antiviral therapy. AIDS 12(5):461–5CrossRefGoogle Scholar
  37. Richman DD, Margolis DM, Delaney M, Greene WC, Hazuda D, Pomerantz RJ (2009) The challenge of finding a cure for HIV infection. Science 323(5919):1304–7. CrossRefGoogle Scholar
  38. Ruelas DS, Greene WC (2013) An integrated overview of HIV-1 latency. Cell 155(3):519–29. CrossRefGoogle Scholar
  39. Siliciano JD, Kajdas J, Finzi D, Quinn TC, Chadwick K, Margolick JB, Kovacs C, Gange SJ, Siliciano RF (2003) Long-term follow-up studies confirm the stability of the latent reservoir for HIV-1 in resting CD4+ T cells. Nat Med 9(6):727–8. CrossRefGoogle Scholar
  40. Sultan B, Benn P, Waters L (2014) Current perspectives in HIV post-exposure prophylaxis. HIV AIDS (Auckl) 6:147–58. Google Scholar
  41. Whitney JB, Hill AL, Sanisetty S, Penaloza-MacMaster P, Liu J, Shetty M, Parenteau L, Cabral C, Shields J, Blackmore S, Smith JY, Brinkman AL, Peter LE, Mathew SI, Smith KM, Borducchi EN, Rosenbloom DIS, Lewis MG, Hattersley J, Li B, Hesselgesser J, Geleziunas R, Robb ML, Kim JH, Michael NL, Barouch DH (2014) Rapid seeding of the viral reservoir prior to SIV viraemia in rhesus monkeys. Nature 512(7512):74–7. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAssiut UniversityAssiutEgypt
  2. 2.Department of Mathematics and Institute of Applied MathematicsUniversity of British ColumbiaVancouverCanada

Personalised recommendations