Bacteriophage Infection Dynamics: Multiple Host Binding Sites

H. L. Smith; R. T. Trevino

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 6, page 109-134
  • ISSN: 0973-5348

Abstract

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We construct a stochastic model of bacteriophage parasitism of a host bacteria that accounts for demographic stochasticity of host and parasite and allows for multiple bacteriophage adsorption to host. We analyze the associated deterministic model, identifying the basic reproductive number for phage proliferation, showing that host and phage persist when it exceeds unity, and establishing that the distribution of adsorbed phage on a host is binomial with slowly evolving mean. Not surprisingly, extinction of the parasite or both host and parasite can occur for the stochastic model.

How to cite

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Smith, H. L., and Trevino, R. T.. "Bacteriophage Infection Dynamics: Multiple Host Binding Sites." Mathematical Modelling of Natural Phenomena 4.6 (2009): 109-134. <http://eudml.org/doc/222284>.

@article{Smith2009,
abstract = { We construct a stochastic model of bacteriophage parasitism of a host bacteria that accounts for demographic stochasticity of host and parasite and allows for multiple bacteriophage adsorption to host. We analyze the associated deterministic model, identifying the basic reproductive number for phage proliferation, showing that host and phage persist when it exceeds unity, and establishing that the distribution of adsorbed phage on a host is binomial with slowly evolving mean. Not surprisingly, extinction of the parasite or both host and parasite can occur for the stochastic model. },
author = {Smith, H. L., Trevino, R. T.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {bacteriophage; stochastic simulation algorithm; phage adsorption; persistence; basic reproductive number; stochastic simulation algorithm},
language = {eng},
month = {11},
number = {6},
pages = {109-134},
publisher = {EDP Sciences},
title = {Bacteriophage Infection Dynamics: Multiple Host Binding Sites},
url = {http://eudml.org/doc/222284},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Smith, H. L.
AU - Trevino, R. T.
TI - Bacteriophage Infection Dynamics: Multiple Host Binding Sites
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/11//
PB - EDP Sciences
VL - 4
IS - 6
SP - 109
EP - 134
AB - We construct a stochastic model of bacteriophage parasitism of a host bacteria that accounts for demographic stochasticity of host and parasite and allows for multiple bacteriophage adsorption to host. We analyze the associated deterministic model, identifying the basic reproductive number for phage proliferation, showing that host and phage persist when it exceeds unity, and establishing that the distribution of adsorbed phage on a host is binomial with slowly evolving mean. Not surprisingly, extinction of the parasite or both host and parasite can occur for the stochastic model.
LA - eng
KW - bacteriophage; stochastic simulation algorithm; phage adsorption; persistence; basic reproductive number; stochastic simulation algorithm
UR - http://eudml.org/doc/222284
ER -

References

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  1. E. Beretta, Y. Kuang. Modeling and analysis of a marine bacteriophage infection. Math. Biosci., 149(1998), 57–76.  
  2. 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.  
  3. 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.  
  4. 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.  
  5. A. Campbell. Conditions for existence of bacteriophages. Evolution, 15(1961), 153–165.  
  6. M. Carletti. Mean-square stability of a stochastic model for bacteriophage infection with time delays. Mathematical Biosciences, 210(2007), 395-414.  
  7. J. Carr. Applications of centre manifold theory. Springer-Verlag, New York, 1981.  
  8. P. DeLeenheer and H.L. Smith. Virus dynamics: a global analysis. SIAM J. Appl. Math., 63(2003), 1313–1327.  
  9. 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.  
  10. E. Ellis and M. Delbrück. The growth of bacteriophage. J. of Physiology, 22(1939), 365–384.  
  11. D. Gillespie. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81 (1977), No. 25, 2340–2361, 1977.  
  12. Y. Cao, D. Gillespie, L. Petzold. The slow-scale stochastic simulation algorithm. J. Chem. Physics, 122 (2005), 014116.  
  13. P. Grayson, L. Han, T. Winther, R. Phillips. Real-time observations of single bacteriophage lambda DNA ejection in vitro. PNAS, 104 (2007), No. 37, 14652–57.  
  14. 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.  
  15. 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.  
  16. B. Levin, J. Bull. Phage therapy revisited: the population biology of a bacterial infection and its treatment with bacteriophage and antibiotics. Amer. Nat., 147 (1996), 881–898.  
  17. B. Levin, J. Bull. Population and evolutionary dynamics of phage therapy. Nature Reviews Microbiology, 2 (2004), 166–173.  
  18. M. Kretzschmar and F. Adler. Aggregated distributions in models for patchy populations. Theor. Pop. Biol., 43 (1993), 1–30.  
  19. A.P. Krueger. The sorption of bacteriophage by living and dead susceptible bacteria: I. Equilibrium Conditions. J. Gen. Physiol., 14 (1931), 493–516.  
  20. 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.  
  21. M.A. Nowak and R.M. May. Virus dynamics. Oxford University Press, New York, 2000.  
  22. R. Payne, V. Jansen. Understanding bacteriophage therapy as a density-dependent kinetic process. J. Theor. Biol., 208 (2001), 37–48.  
  23. R. Payne and V. Jansen. Pharmacokinetic principles of bacteriophage therapy. Clin. Pharmacokinetics, 42 (2003), No. 4, 315–325.  
  24. A.S. Perelson and P.W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41 (1999), 3–44.  
  25. H.L. Smith. Models of virulent phage growth with application to phage therapy. SIAM J. Appl. Math., 68 (2008), 1717–1737.  
  26. S.J. Schrag and J.E. Mittler. Host-parasite coexistence: the role of spatial refuges in stabilizing bacteria-phage interactions. Amer. Nat., 148 (1996), 348–377.  
  27. G. Stent. Molecular biology of bacterial viruses. W.H. Freeman and Co., London, 1963.  
  28. H. R. Thieme. Persistence under relaxed point-dissipativity (with applications to an endemic model). SIAM J. Math. Anal., 24 (1993), 407–435.  
  29. H.R. Thieme and J. Yang. On the Complex formation approach in modeling predator prey relations, mating, and sexual disease transmission. Elect. J. Diff. Eqns., 05 (2000), 255–283.  
  30. R. Weld, C. Butts, J. Heinemann. Models of phage growth and their applicability to phage therapy. J. Theor. Biol., 227 (2004), 1–11.  
  31. X.-Q. Zhao. Dynamical systems in population biology. CMS Books in Mathematics, Springer, 2003.  

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