Simulation Study of HIV Temporal Patterns Using Bayesian Methodology

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 296)


Viral load values and CD4\(^{+}\)T cells count are markers currently evaluated in the clinical follow-up of HIV/AIDS patients. In this context, it is relevant to develop methods that provide a more complete temporal description of these markers, e.g. in between clinical appointments. To this end, we combine a mathematical model and a Bayesian methodology to estimate trajectories from a set of observed values. Also, we construct a variation band containing the most central trajectories for one patient, by exploring the range of values in the a posteriori distributions. The methods are illustrated with simulated data.


Bayesian statistics Human immunodeficiency virus (HIV) Mathematical models Nonlinear programming Parameter estimation 



This work was partially funded by the Foundation for Science and Technology, FCT, through national (MEC) and European structural (FEDER) funds, in the scope of UID/MAT/04106/2019 (CIDMA/UA), UID/CEC/00127/2019 (IEETA/UA) and UID/MAT/00144/2019 (CMUP/UP) projects. Diana Rocha acknowledges the FCT grant (ref. SFRH/BD/107889/2015). This work was also partially funded by Portugal 2020 under the Competitiveness and Internationalization Operational Program, and by the European Regional Development Fund through project SOCA-Smart Open Campus (CENTRO-01-0145-FEDER-000010).


  1. 1.
    Bonhoeffer, S., May, R.M., Shaw, G.M., Nowak, M.A.: Virus dynamics and drug therapy. Proc. Natl. Acad. Sci. USA 94, 6971–6976 (1997)CrossRefGoogle Scholar
  2. 2.
    Gelman, A., Rubin, D.B.: Inference from iterative simulation using multiple sequences. Stat. Sci. 169, 457–472 (1992)CrossRefGoogle Scholar
  3. 3.
    Geweke, J.: Evaluating the accuracy of sampling based approaches to the calculation of posterior moments. Bayesian Stat. 4, 169–193 (1992)MathSciNetGoogle Scholar
  4. 4.
    Hadjiandreou, M.M., Conejeros, R., Wilson, D.I.: Long-term HIV dynamics subject to continuous therapy and structured treatment interruptions. Chem. Eng. Sci. 64, 1600–1617 (2009)CrossRefGoogle Scholar
  5. 5.
    Huang, Y., Liu, D., Wu, H.: Hierarchical bayesian methods for estimation of parameters in a longitudinal HIV dynamic system. Biometrics 62, 413–423 (2006)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Huang, Y., Wu, H., Acosta, E.P.: Hierarchical bayesian inference for HIV dynamic differential equation models incorporating multiple treatment factors. Biom. J. 52, 470–486 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Liang, H., Miao, H., Wu, H.: Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model. Ann. Appl. Stat. 4, 460483 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Nowak, M.A., May, R.M.: Virus Dynamics: Mathematical Principles of Immunology and Virology. Oxford University Press, Oxford (2000)zbMATHGoogle Scholar
  9. 9.
    Perelson, A.S.: Modelling viral and immune system dynamics. Nat. Rev. Immunol. 2, 28–36 (2002)CrossRefGoogle Scholar
  10. 10.
    Perelson, A.S., Kirschner, D.E., Boer, R.: Dynamics of HIV infection of CD4\(^+\)T cells. Math. Biosci. 114, 81–125 (1993)Google Scholar
  11. 11.
    Rocha, D., Gouveia, S., Pinto, C., Scotto, M., Tavares, J.N., Valadas, E., Caldeira, L.F.: On the parameters estimation of HIV dynamic models. In: Proceedings of the III Portuguese-Galician Meeting of Biometry (EBIO2018), University of Aveiro, Portugal, June 28–30, pp. 57–60 (2018)Google Scholar
  12. 12.
    Stafford, M.A., Coreya, L., Caob, Y., Daardd, E.S., Hob, D.D., Perelson, A.S.: Modeling plasma virus concentration during primary HIV infection. J. Theor. Biol. 203, 285–301 (2000)CrossRefGoogle Scholar
  13. 13.
    Whitby, L., Whitby, A., Fletcher, M., Helbert, M., Reilly, J.T., Barnett, D.: Comparison of methodological data measurement limits in CD4\(^+\)T lymphocyte flow cytometric enumeration and their clinical impact on HIV management. Cytom. Part B (Clin. Cytom.) 84, 248–254 (2013)CrossRefGoogle Scholar
  14. 14.
    Wu, L.: A joint model for nonlinear mixed-effects models with censoring and covariates measured with error, with application to AIDS studies. J. Am. Stat. Assoc. 97, 955–964 (2002)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Center for R&D in Mathematics and Applications (CIDMA)University of Aveiro (UA)AveiroPortugal
  2. 2.CEMAT and Department of Mathematics, ISTUniversity of LisbonLisbonPortugal
  3. 3.School of Engineering, Polytechnic of PortoPortoPortugal
  4. 4.Centre of Mathematics of the University of Porto - CMUPPortoPortugal
  5. 5.Centre of Mathematics of the University of Porto - CMUPPortoPortugal
  6. 6.Center for R&D in Mathematics and Applications (CIDMA)University of Aveiro (UA)AveiroPortugal
  7. 7.Institute of Electronics and Informatics Engineering of Aveiro, IEETA, UAAveiroPortugal

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