de Rioja, Victor Lopez

Fort, Joaquim

Isern, Neus

English

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The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and ApplicationSpread of virus infections  V. L. de Rioja1*, J. Fort1, N. Isern1  1Universitat de Girona, Girona, Spain. victor.lopezd@udg.edu  We propose a new reaction-diffusion set of equations to explain the spread of viruses on bacterial populations. Although the process  , (1)was first described years ago [1] and several modifications have been proposed since then [2-5], in this new model we introduce improvements. The two main features of the model are: (i) the second-order correction in time that takes care of the time delay due to the fact that viruses spend a time τ inside the cells before the new generation disperses away [4, 5], and (ii) a new mathematical formulation for the death of infected cells, also dependent on the time delay τ, and which is biologically more reasonable than other approaches using a logistic equation [4, 5]. We apply our model to experimental data for the front propagation speed of several T7 virus strains [6], calculating the necessary parameters from independent experiments (as opposed to other authors [2, 3, 7, 8]). We find good agreement between the model and experimental data. We compare our results to a classical model with no time delay by Yin and McCaskill [2], as well as to two models that describe the death process similarly to our approach but without the including the diffusive delay [7, 8]. All the other models overestimate the measured speed, therefore showing that our improvements are not only biologically sound, but also necessary to properly describe the processes of virus infection.  References [1] A.L. Koch: The growth of viral plaques during the enlargement phase. J. Theor. Biol., 6 413 (1964). [2] J. Yin, J.S. McCaskill: Replication of viruses in a growing plaque: a reaction-diffusion model. Biophys. J., 61 1540-1549 (1992). [3] L. You, J. Yin: Amplification and spread of viruses in a growing plaque. J. Theor. Biol., 200 365-373 (1999). [4] J. Fort, V. Méndez: Time-delayed spread of viruses in growing plaques. Phys. Rev. Lett., 89 178101 1-4 (2002). [5] D.R. Amor, J. Fort: Virus infection speeds: theory versus experiment. Phys. Rev. E, 82 061905 1-9 (2010). [6] J. Yin: Evolution of bacteriophage T7 in a growing plaque. J. Bacteriol., 175(5) 1272-1277 (1993). [7] A. Jones, H.L. Smith, H.R. Thieme, G. Röst: On spread of phage infection of bacteria in a petri dish. SIAM J. Appl. Math., 72 (2) 670-688 (2012). [8] S.A. Gourley, Y. Kuang: A delay reaction-diffusion model of the spread of bacteriophage infection. SIAM J. Appl. Math., 65 (2) 550-566 (2005). This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/1

Spread of virus infections

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Spread of virus infections

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