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Impacts of the Cell-Free and Cell-to-Cell Infection Modes on Viral Dynamics

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Abstract

Virus can disseminate between uninfected target cells via two modes, namely, the diffusion-limited cell-free viral spread and the direct cell-to-cell transfer using virological synapses. To examine how these two viral infection modes impact the viral dynamics, in this paper, we propose and analyze a general viral infection model that incorporates these two viral infection modes. The model also includes nonlinear target-cell dynamics, infinitely distributed intracellular delays, nonlinear incidences, and concentration-dependent clearance rates. It is shown that the numbers of secondly infected cells through the cell-free infection mode and the cell-to-cell infection mode both contribute to the basic reproduction number. Under some reasonable assumptions, the model exhibits a global threshold dynamics: the infection is cleared out if the basic reproduction number is less than one and the infection persists if the basic reproduction number is larger than one. Two specific examples are provided to illustrate that our theoretical results cover and improve some existing ones. When the underlying assumptions are not satisfied, oscillations via global Hopf bifurcation can be observed. A brief simulation of two-parameter bifurcation analysis is given to explore the joint impacts on viral dynamics for the interplay between nonlinear target-cell dynamics and intracellular delays.

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Acknowledgements

The authors are very grateful to one anonymous referee for his/her valuable comments and suggestions, which greatly improved the presentation of this work. H. Shu was partially supported by the National Natural Science Foundation of China (No.11601392), Pujiang Talent Program of Shanghai (No. 16PJ1409100) and the Fundamental Research Funds for the Central Universities, Y. Chen and L. Wang were partially supported by NSERC.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Hongying Shu

  2. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada

    Yuming Chen

  3. Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Lin Wang

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  1. Hongying Shu
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Correspondence to Hongying Shu.

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Shu, H., Chen, Y. & Wang, L. Impacts of the Cell-Free and Cell-to-Cell Infection Modes on Viral Dynamics. J Dyn Diff Equat 30, 1817–1836 (2018). https://doi.org/10.1007/s10884-017-9622-2

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  • DOI: https://doi.org/10.1007/s10884-017-9622-2

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