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[J]. Mathematical Biosciences and Engineering, 2014, 11(5): 1091-1113. doi: 10.3934/mbe.2014.11.1091
Related Papers:
[1] |
Sukhitha W. Vidurupola, Linda J. S. Allen .
Basic stochastic models for viral infection within a host. Mathematical Biosciences and Engineering, 2012, 9(4): 915-935.
doi: 10.3934/mbe.2012.9.915
|
[2] |
Chen Liang, Hai-Feng Huo, Hong Xiang .
Modelling mosquito population suppression based on competition system with strong and weak Allee effect. Mathematical Biosciences and Engineering, 2024, 21(4): 5227-5249.
doi: 10.3934/mbe.2024231
|
[3] |
Diego Vicencio, Olga Vasilieva, Pedro Gajardo .
Monotonicity properties arising in a simple model of Wolbachia invasion for wild mosquito populations. Mathematical Biosciences and Engineering, 2023, 20(1): 1148-1175.
doi: 10.3934/mbe.2023053
|
[4] |
A. M. Elaiw, Raghad S. Alsulami, A. D. Hobiny .
Global dynamics of IAV/SARS-CoV-2 coinfection model with eclipse phase and antibody immunity. Mathematical Biosciences and Engineering, 2023, 20(2): 3873-3917.
doi: 10.3934/mbe.2023182
|
[5] |
Tae Jin Lee, Jose A. Vazquez, Arni S. R. Srinivasa Rao .
Mathematical modeling of impact of eCD4-Ig molecule in control and management of HIV within a host. Mathematical Biosciences and Engineering, 2021, 18(5): 6887-6906.
doi: 10.3934/mbe.2021342
|
[6] |
Khalid Hattaf, Noura Yousfi .
Dynamics of SARS-CoV-2 infection model with two modes of transmission and immune response. Mathematical Biosciences and Engineering, 2020, 17(5): 5326-5340.
doi: 10.3934/mbe.2020288
|
[7] |
Nada Almuallem, Dumitru Trucu, Raluca Eftimie .
Oncolytic viral therapies and the delicate balance between virus-macrophage-tumour interactions: A mathematical approach. Mathematical Biosciences and Engineering, 2021, 18(1): 764-799.
doi: 10.3934/mbe.2021041
|
[8] |
Jinhu Xu .
Dynamic analysis of a cytokine-enhanced viral infection model with infection age. Mathematical Biosciences and Engineering, 2023, 20(5): 8666-8684.
doi: 10.3934/mbe.2023380
|
[9] |
Zizi Wang, Zhiming Guo, Hal Smith .
A mathematical model of oncolytic virotherapy with time delay. Mathematical Biosciences and Engineering, 2019, 16(4): 1836-1860.
doi: 10.3934/mbe.2019089
|
[10] |
Andrei Korobeinikov, Conor Dempsey .
A continuous phenotype space model of RNA virus evolution within a host. Mathematical Biosciences and Engineering, 2014, 11(4): 919-927.
doi: 10.3934/mbe.2014.11.919
|
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.
References
[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.
|