Dynamics of evolutionary competition between budding and lytic viral release strategies

Xiulan Lai; Xingfu Zou

doi:10.3934/mbe.2014.11.1091

Article Contents

2014, Volume 11, Issue 5: 1091-1113. Doi: 10.3934/mbe.2014.11.1091

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Dynamics of evolutionary competition between budding and lytic viral release strategies

Xiulan Lai^1, and
Xingfu Zou^2,

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

Received: December 31, 2013

Revised: March 31, 2014

Published: May 2014

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Abstract

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.

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

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