Mathematical Biosciences and Engineering, 2014, 11(5): 1091-1113. doi: 10.3934/mbe.2014.11.1091.

Primary: 34K20, 92B05; Secondary: 34K25, 92D25.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Dynamics of evolutionary competition between budding and lytic viral release strategies

1. Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 5B7
2. Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7

In this paper, we consider the evolutionary competition between budding and lytic viral release strategies, using a delay differential equation model with distributed delay. When antibody is not established, the dynamics of competition depends on the respective basic reproductive ratios of the two viruses. If the basic reproductive ratio of budding virus is greater than that of lytic virus and one, budding virus can survive. When antibody is established for both strains but the neutralization capacities are the same for both strains, consequence of the competition also depends only on the basic reproductive ratios of the budding and lytic viruses. Using two concrete forms of the viral production functions, we are also able to conclude that budding virus will outcompete if the rates of viral production, death rates of infected cells and neutralizing capacities of the antibodies are the same for budding and lytic viruses. In this case, budding strategy would have an evolutionary advantage. However, if the antibody neutralization capacity for the budding virus is larger than that for the lytic virus, the lytic virus can outcompete the budding virus provided that its reproductive ratio is very high. An explicit threshold is derived.
  Article Metrics

Keywords competition; stability; antibody; infection age; releasing strategy; burst size.; budding; Virus dynamics; lytic

Citation: Xiulan Lai, Xingfu Zou. Dynamics of evolutionary competition between budding and lytic viral release strategies. Mathematical Biosciences and Engineering, 2014, 11(5): 1091-1113. doi: 10.3934/mbe.2014.11.1091


  • 1. Proc. R. Soc. B., 272 (2005), 2065-2072.
  • 2. John Wiley and Sons, Ltd, 2007.
  • 3. in Mathematical Population Dynamics: Analysis of Heterogeneity, I. Theory of Epidemics (eds. O. Arino, et al.), Wuerz, Winnnipeg, 1995, 33-50.
  • 4. Bull. Math. Biol., 65 (2003), 1003-1023.
  • 5. Microbiology and Moleculer Biology Reviews, 62 (1998), 1171-1190.
  • 6. J. Theor. Biol. 229 (2004), 281-288.
  • 7. Springer-Verlag, New York, 1993.
  • 8. J. Theor. Biol., 249 (2007), 766-784.
  • 9. Virus Research, 106 (2004), 147-165.
  • 10. Math. Biosci. Eng., 1 (2004), 267-288.
  • 11. J. Appl. Math., 67 (2007), 731-756.
  • 12. Mathematical Surveys and Monographs, 41, AMS, Providence, 1995.
  • 13. Evolutionary Ecology, 10 (1996), 545-558.
  • 14. Genetics, 172 (2006), 17-26.


This article has been cited by

  • 1. Jinliang Wang, Jiying Lang, Xingfu Zou, Analysis of an age structured HIV infection model with virus-to-cell infection and cell-to-cell transmission, Nonlinear Analysis: Real World Applications, 2017, 34, 75, 10.1016/j.nonrwa.2016.08.001
  • 2. Shaoli Wang, Jianhong Wu, Libin Rong, A note on the global properties of an age-structured viral dynamic model with multiple target cell populations, Mathematical Biosciences and Engineering, 2016, 14, 3, 805, 10.3934/mbe.2017044
  • 3. Cameron Browne, Immune response in virus model structured by cell infection-age, Mathematical Biosciences and Engineering, 2016, 13, 5, 887, 10.3934/mbe.2016022
  • 4. Yan Wang, Kaihui Liu, Yijun Lou, An age-structured within-host HIV model with T-cell competition, Nonlinear Analysis: Real World Applications, 2017, 38, 1, 10.1016/j.nonrwa.2017.04.002
  • 5. Eric Numfor, Optimal treatment in a multi-strain within-host model of HIV with age structure, Journal of Mathematical Analysis and Applications, 2019, 123410, 10.1016/j.jmaa.2019.123410

Reader Comments

your name: *   your email: *  

Copyright Info: 2014, Xiulan Lai, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved