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Bacteriophage Infection Dynamics: Multiple Host BindingSites

Published online by Cambridge University Press:  27 November 2009

H. L. Smith  and
R. T. Trevino
H. L. Smith*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, 85287 Tempe, AZ, USA
R. T. Trevino
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, 85287 Tempe, AZ, USA
*
halsmith@asu.edu
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Abstract

We construct a stochastic model ofbacteriophage parasitism of a host bacteria that accounts fordemographic stochasticity of host and parasite and allows formultiple bacteriophage adsorption to host. We analyze the associateddeterministic model, identifying the basic reproductive number forphage proliferation, showing that host and phage persist when itexceeds unity, and establishing that the distribution of adsorbedphage on a host is binomial with slowly evolving mean. Notsurprisingly, extinction of the parasite or both host and parasitecan occur for the stochastic model.

Keywords

bacteriophagestochastic simulationalgorithmphage adsorptionpersistencebasic reproductive number
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 6: Ecology (Part 1) , 2009 , pp. 109 - 134
Copyright
© EDP Sciences, 2009

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References

E. Beretta, Y. Kuang. Modeling and analysis of a marine bacteriophage infection. Math. Biosci., 149(1998), 57–76.
B.J.M. Bohannan and R.E. Lenski. Effect of prey heterogeneity on the response of a model food chain to resource enrichment. The American Nat., 153(1999), 73–82.
B.J.M. Bohannan and R.E. Lenski. Linking genetic change to community evolution: insights from studies of bacteria and bacteriophage. Ecology Letters, 3(2000), 362–377.
B.J. Cairns, A.R. Timms, V.A.A. Jansen. I.F. Connerton, R.J.H. Payne, Quantitative models of in vitro bacteriophage-host dynamics and their application to phage therapy. PLOS Pathogens, 5(2009), e1000253.
A. Campbell. Conditions for existence of bacteriophages. Evolution, 15(1961), 153–165.
M. Carletti. Mean-square stability of a stochastic model for bacteriophage infection with time delays. Mathematical Biosciences, 210(2007), 395-414.
J. Carr. Applications of centre manifold theory. Springer-Verlag, New York, 1981.
P. DeLeenheer and H.L. Smith. Virus dynamics: a global analysis. SIAM J. Appl. Math., 63(2003), 1313–1327.
M. De Paepe and F. Taddei. Viruses' life history: towards a mechanistic basis of a trade-off between survival and reproduction among phages. PLOS Biol., 4(2006), 1248–1256.
E. Ellis and M. Delbrück. The growth of bacteriophage. J. of Physiology, 22(1939), 365–384.
D. Gillespie. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81 (1977), No. 25, 2340–2361, 1977.
Cao, Y., Gillespie, D., Petzold, L.. The slow-scale stochastic simulation algorithm. J. Chem. Physics, 122 (2005), 014116. CrossRef
Grayson, P., Han, L., Winther, T., Phillips, R.. Real-time observations of single bacteriophage lambda DNA ejection in vitro. PNAS, 104 (2007), No. 37, 14652–57. CrossRef
B. Levin, F. Stewart, L. Chao, Resource-limited growth, competition, and predation: a model and experimental studies with bacteria and bacteriophage, Amer. Nat., 111 (1977), 3–24.
R. Lenski and B. Levin. Constraints on the coevolution of bacteria and virulent phage: a model, some experiments, and predictions for natural communities, Amer. Nat., 125 (1985), No. 4, 585–602.
Levin, B., Bull, J.. Phage therapy revisited: the population biology of a bacterial infection and its treatment with bacteriophage and antibiotics. Amer. Nat., 147 (1996), 881–898. CrossRef
Levin, B., Bull, J.. Population and evolutionary dynamics of phage therapy. Nature Reviews Microbiology, 2 (2004), 166–173. CrossRef
Kretzschmar, M. and Adler, F.. Aggregated distributions in models for patchy populations. Theor. Pop. Biol., 43 (1993), 1–30. CrossRef
Krueger, A.P.. The sorption of bacteriophage by living and dead susceptible bacteria: I. Equilibrium Conditions. J. Gen. Physiol., 14 (1931), 493–516. CrossRef
S. Matsuzaki, M. Rashel, J. Uchiyama, S. Sakurai, T. Ujihara, M. Kuroda, M. Ikeuchi, T. Tani, M. Fujieda, H. Wakiguchi, S. Imai, Bacteriophage therapy: a revitalized therapy against bacterial infectious diseases. J. Infect. Chemother., 11(2005), 211–219.
M.A. Nowak and R.M. May. Virus dynamics. Oxford University Press, New York, 2000.
Payne, R., Jansen, V.. Understanding bacteriophage therapy as a density-dependent kinetic process. J. Theor. Biol., 208 (2001), 37–48. CrossRef
Payne, R. and Jansen, V.. Pharmacokinetic principles of bacteriophage therapy. Clin. Pharmacokinetics, 42 (2003), No. 4, 315–325. CrossRef
A.S. Perelson and P.W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41 (1999), 3–44.
Smith, H.L.. Models of virulent phage growth with application to phage therapy. SIAM J. Appl. Math., 68 (2008), 1717–1737. CrossRef
Schrag, S.J. and Mittler, J.E.. Host-parasite coexistence: the role of spatial refuges in stabilizing bacteria-phage interactions. Amer. Nat., 148 (1996), 348–377. CrossRef
G. Stent. Molecular biology of bacterial viruses. W.H. Freeman and Co., London, 1963.
Thieme, H. R.. Persistence under relaxed point-dissipativity (with applications to an endemic model). SIAM J. Math. Anal., 24 (1993), 407–435. CrossRef
Thieme, H.R. and Yang, J.. On the Complex formation approach in modeling predator prey relations, mating, and sexual disease transmission. Elect. J. Diff. Eqns., 05 (2000), 255–283.
Weld, R., Butts, C., Heinemann, J.. Models of phage growth and their applicability to phage therapy. J. Theor. Biol., 227 (2004), 1–11. CrossRef
X.-Q. Zhao. Dynamical systems in population biology. CMS Books in Mathematics, Springer, 2003.