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

## Dynamics of evolutionary competition between budding and lytic viral release strategies

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

Received  January 2014 Revised  April 2014 Published  June 2014

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.
Citation: Xiulan Lai, Xingfu Zou. Dynamics of evolutionary competition between budding and lytic viral release strategies. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1091-1113. doi: 10.3934/mbe.2014.11.1091
##### References:
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##### References:
 [1] A. Brännstr$\ddot o$m and D. J. T. Sumpter, The role of competition and clustering in population dynamics,, Proc. R. Soc. B., 272 (2005), 2065. Google Scholar [2] J. Carter and V. Saunders, Virology: Principles and Application,, John Wiley and Sons, (2007). Google Scholar [3] C. Castillo-Chaves and H. R. Thieme, Asymptotically autonomous epidemic models,, in Mathematical Population Dynamics: Analysis of Heterogeneity, (1995), 33. Google Scholar [4] D. Coombs, Optimal viral production,, Bull. Math. Biol., 65 (2003), 1003. doi: 10.1016/S0092-8240(03)00056-9. Google Scholar [5] H. Garoff, R. Hewson and D. Opstelten, Virus maturation by budding,, Microbiology and Moleculer Biology Reviews, 62 (1998), 1171. Google Scholar [6] M. A. Gilchrist, D. Coombs and A. S. Perelson, Optimizing within-host viral fitness: Infected cell lifespan and virion production rate,, J. Theor. Biol. 229 (2004), 229 (2004), 281. doi: 10.1016/j.jtbi.2004.04.015. Google Scholar [7] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations,, Springer-Verlag, (1993). doi: 10.1007/978-1-4612-4342-7. Google Scholar [8] N. L. Komarova, Viral reproductive strategies: How can lytic viruses be evolutionarily competitive?, J. Theor. Biol., 249 (2007), 766. doi: 10.1016/j.jtbi.2007.09.013. Google Scholar [9] D. P. Nayak, Assembly and budding of influenza virus,, Virus Research, 106 (2004), 147. doi: 10.1016/j.virusres.2004.08.012. Google Scholar [10] P. W. Nelson, M. A. Gilchrist, D. Coombs, J. M. Hyman and A. S. Perelson, An age-structured model of HIV infection that allows for variation in the production rate of viral particles and the death rate of productively infected cells,, Math. Biosci. Eng., 1 (2004), 267. doi: 10.3934/mbe.2004.1.267. Google Scholar [11] L. Rong, Z. Feng and A. S. Perelson, Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy,, J. Appl. Math., 67 (2007), 731. doi: 10.1137/060663945. Google Scholar [12] H. L. Smith, Monotone Dynamical Systems. An Introduction To The Theory Of Competitive And Cooperative Systems,, Mathematical Surveys and Monographs, (1995). Google Scholar [13] I. N. Wang, D. E. Dykhuizen and L. B. Slobodkin, The evolution of phage lysis timing,, Evolutionary Ecology, 10 (1996), 545. doi: 10.1007/BF01237884. Google Scholar [14] I. N. Wang, Lysis timing and bacteriophage fitness,, Genetics, 172 (2006), 17. doi: 10.1534/genetics.105.045922. Google Scholar
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