# American Institute of Mathematical Sciences

• Previous Article
What can mathematical models tell us about the relationship between circular migrations and HIV transmission dynamics?
• MBE Home
• This Issue
• Next Article
Transmission dynamics and control for a brucellosis model in Hinggan League of Inner Mongolia, China
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:
 [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

show all references

##### 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
 [1] Yu Yang, Shigui Ruan, Dongmei Xiao. Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function. Mathematical Biosciences & Engineering, 2015, 12 (4) : 859-877. doi: 10.3934/mbe.2015.12.859 [2] Fred Brauer. Age-of-infection and the final size relation. Mathematical Biosciences & Engineering, 2008, 5 (4) : 681-690. doi: 10.3934/mbe.2008.5.681 [3] Cameron Browne. Immune response in virus model structured by cell infection-age. Mathematical Biosciences & Engineering, 2016, 13 (5) : 887-909. doi: 10.3934/mbe.2016022 [4] Hossein Mohebbi, Azim Aminataei, Cameron J. Browne, Mohammad Reza Razvan. Hopf bifurcation of an age-structured virus infection model. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 861-885. doi: 10.3934/dcdsb.2018046 [5] Hui li, Manjun Ma. Global dynamics of a virus infection model with repulsive effect. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4783-4797. doi: 10.3934/dcdsb.2019030 [6] Alexander Rezounenko. Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1547-1563. doi: 10.3934/dcdsb.2017074 [7] Fred Brauer, Zhisheng Shuai, P. van den Driessche. Dynamics of an age-of-infection cholera model. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1335-1349. doi: 10.3934/mbe.2013.10.1335 [8] Jinliang Wang, Ran Zhang, Toshikazu Kuniya. A note on dynamics of an age-of-infection cholera model. Mathematical Biosciences & Engineering, 2016, 13 (1) : 227-247. doi: 10.3934/mbe.2016.13.227 [9] Yuming Chen, Junyuan Yang, Fengqin Zhang. The global stability of an SIRS model with infection age. Mathematical Biosciences & Engineering, 2014, 11 (3) : 449-469. doi: 10.3934/mbe.2014.11.449 [10] Steffen Eikenberry, Sarah Hews, John D. Nagy, Yang Kuang. The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth. Mathematical Biosciences & Engineering, 2009, 6 (2) : 283-299. doi: 10.3934/mbe.2009.6.283 [11] Bao-Zhu Guo, Li-Ming Cai. A note for the global stability of a delay differential equation of hepatitis B virus infection. Mathematical Biosciences & Engineering, 2011, 8 (3) : 689-694. doi: 10.3934/mbe.2011.8.689 [12] Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva. Global dynamics of a vector-host epidemic model with age of infection. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1159-1186. doi: 10.3934/mbe.2017060 [13] Folashade B. Agusto. Optimal control and cost-effectiveness analysis of a three age-structured transmission dynamics of chikungunya virus. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 687-715. doi: 10.3934/dcdsb.2017034 [14] Zhaohui Yuan, Xingfu Zou. Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays. Mathematical Biosciences & Engineering, 2013, 10 (2) : 483-498. doi: 10.3934/mbe.2013.10.483 [15] Hongying Shu, Lin Wang. Global stability and backward bifurcation of a general viral infection model with virus-driven proliferation of target cells. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1749-1768. doi: 10.3934/dcdsb.2014.19.1749 [16] Nicola Bellomo, Youshan Tao. Stabilization in a chemotaxis model for virus infection. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 105-117. doi: 10.3934/dcdss.2020006 [17] Jinliang Wang, Jiying Lang, Yuming Chen. Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3721-3747. doi: 10.3934/dcdsb.2017186 [18] Jinliang Wang, Xiu Dong. Analysis of an HIV infection model incorporating latency age and infection age. Mathematical Biosciences & Engineering, 2018, 15 (3) : 569-594. doi: 10.3934/mbe.2018026 [19] Pavol Bokes. Maintaining gene expression levels by positive feedback in burst size in the presence of infinitesimal delay. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5539-5552. doi: 10.3934/dcdsb.2019070 [20] Carlota Rebelo, Alessandro Margheri, Nicolas Bacaër. Persistence in some periodic epidemic models with infection age or constant periods of infection. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1155-1170. doi: 10.3934/dcdsb.2014.19.1155

2018 Impact Factor: 1.313