Abstract
Viruses reproduce by multiplying within host cells. The reproductive fitness of a virus is proportional to the number of offspring it can produce during the lifetime of the cell it infects. If viral production rates are independent of cell death rate, then one expects natural selection will favor viruses that maximize their production rates. However, if increases in the viral production rate lead to an increase in the cell death rate, then the viral production rate that maximizes fitness may be less than the maximum. Here we pose the question of how fast should a virus replicate in order to maximize the number of progeny virions that it produces. We present a general mathematical framework for studying problems of this type, which may be adapted to many host-parasite systems, and use it to examine the optimal virus production scheduling problem from the perspective of the virus.
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References
Almogy, G., N. Cohen, S. Stocker and L. Stone (2002). Immune response and virus population composition: HIV as a case study. Proc. Roy. Soc. Lond. B269, 809–815.
Bellman, R. (1957). Dynamic Programming, Princeton: Princeton University Press.
Boisvert, J., X.-S. He, R. Cheung, E. B. Keeffe, T. Wright and H. B. Greenberg (2001). Quantitative analysis of hepatitis C virus in peripheral blood and liver: replication detected only in liver. J. Infect. Dis. 184, 827–835.
Bremermann, H. J. and J. Pickering (1983). A game-theoretical model of parasite virulence. J. Theor. Biol. 100, 411–426.
Fenyö, E., L. Morfeldt-Mason, F. Chiodi, B. Lind, A. Von Gegerfelt, J. Albert and B. Åsjö (1988). Distinct replicative and cytopathic characteristics of human immunodeficiency virus isolates. J. Virol. 62, 4414–4419.
Flint, S. J., L. W. Enquist, R. M. Krug, V. R. Racaniello and A. M. Skalka (2000). Principles of Virology, Washington D.C.: American Society for Microbiology.
Furtado, M. R., D. S. Callaway, J. P. Phair, C. A. Macken, A. S. Perelson and S. M. Wolinsky (1999). Persistence of HIV-1 transcription in peripheral-blood mononuclear cells in patients receiving potent antiretroviral therapy. New Engl. J. Med. 340, 1614–1622.
Gilchrist, M.A., D. Coombs and A.S. Perelson. Optimizing Viral Fitness: A Within Host Perspective (submitted).
Grossman, Z. et al. (1999). Ongoing HIV dissemination during HAART. Nat. Med. 5, 1099–1104.
Haase, A. T. et al. (1996). Quantitative image analysis of HIV-1 infection in lymphoid tissue. Science 274, 985–989.
Hockett, R. D., J. M. Kilby, C. A. Derdeyn, M. S. Saag, M. Sillers, K. Squires, S. Chiz, M. A. Nowak, G. M. Shaw and R. P. Bucy (1999). Constant mean viral copy number per infected cell in tissue regardless of high, low, or undetectable plasma HIV RNA. J. Exp. Med. 189, 1545–1554.
Janeway, C. A., P. Travers, M. Walport and M. Shlomchik (2001). Immunobiology, 5th edn, New York: Garland.
May, R. M. and R. M. Anderson (1983). Epidemiology and genetics in the coevolution of parasites and hosts. Proc. Roy. Soc. Lond. B219, 281–313.
Mittler, J. E., B. Sulzer, A. U. Neumann and A. S. Perelson (1998). Influence of delayed virus production on viral dynamics in HIV-1 infected patients. Math. Biosci. 152, 143–163.
Nelson, P. W., J. D. Murray and A. S. Perelson (2000). A model of HIV-1 pathogenesis that includes an intracellular delay. Math. Biosci. 163, 201–215.
Nelson, P. W. and A. S. Perelson (2002). Mathematical analysis of delay differential equation models of HIV-1 infection. Math. Biosci. 179, 73–94.
Nowak, M. A. and R. M. May (2001). Virus Dynamics, Oxford: Oxford University Press.
Perelson, A. S., A. U. Neumann, M. Markowitz, J. M. Leonard and D. D. Ho (1996). HIV-1 dynamics in vivo: virion clearance rate, infected cell lifespan, and viral generation time. Science 271, 1582–1586.
Perelson, A. S. and P. Nelson (1999). Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41, 3–44.
Sasaki, A. and Y. Iwasa (1991). Optimal growth schedule of pathogens within a host: switching between lytic and latent cycles. Theor. Popul. Biol. 39, 201–239.
Zhang, Z.-Q. et al. (1999). Sexual transmission and propagation of SIV and HIV in resting and activated CD4+ T cells. Science 286, 1353–1357.
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Coombs, D., Gilchrist, M.A., Percus, J. et al. Optimal viral production. Bull. Math. Biol. 65, 1003–1023 (2003). https://doi.org/10.1016/S0092-8240(03)00056-9
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DOI: https://doi.org/10.1016/S0092-8240(03)00056-9