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A Delay Mathematical Model for HIV Dynamics in HIV-Specific Helper Cells

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Applied Non-Linear Dynamical Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 93))

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Abstract

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4+ T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4+ T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period for the interval of time for cells, with contact with the virus, to be infected by the virions, released by them; (2) a virion production period for the virions to be produced and released to the bloodstream from the infected cells. We compute the reproduction number of the model, R 0, and the stability of the disease-free equilibrium. We find that for values of R 0 < 1, the model approaches asymptotically the disease-free equilibrium. We present numerical simulations of this fact. These results suggest that the model is mathematically and epidemiologically well posed.

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Acknowledgements

The authors wish to thank Fundação Gulbenkian, through Prémio Gulbenkian de Apoio à Investigação 2003, and the Polytechnic of Porto, through the PAPRE Programa de Apoio à Publicação em Revistas Científicas de Elevada Qualidade, for financial support. CP was partially funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT - Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0144/2013. The research of A.C. was supported by a FCT grant with reference SFRH/BD/96816/2013.

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Authors and Affiliations

  1. Department of Mathematics, School of Engineering, Polytechnic of Porto, Rua Dr António Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    Carla M. A. Pinto

  2. Faculty of Sciences, University of Porto, Rua do Campo Alegre s/n, 4440-452, Porto, Portugal

    Ana R. M. Carvalho

Authors
  1. Carla M. A. Pinto
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  2. Ana R. M. Carvalho
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Correspondence to Carla M. A. Pinto .

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Editors and Affiliations

  1. Department of Automation, Biomechanics and Mechatronics, Łódź University of Technology, Łódź, Poland

    Jan Awrejcewicz

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Pinto, C.M.A., Carvalho, A.R.M. (2014). A Delay Mathematical Model for HIV Dynamics in HIV-Specific Helper Cells. In: Awrejcewicz, J. (eds) Applied Non-Linear Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 93. Springer, Cham. https://doi.org/10.1007/978-3-319-08266-0_35

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