Modeling and analysis of a marine bacteriophage infection

Mathematical Biosciences

Volumn 149, Issue 1, 1998, Pages 57-76

  Beretta, Edoardo ^a   Kuang, Yang ^b  

^a UNIVERSITY OF URBINO   (Italy)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Global stability; Hopf bifurcation; Marine bacteriophage infection; Persistence; Strong uniform repeller

Indexed keywords

BACTERIOPHAGE; MODELLING; VIRAL INFECTION; VIRUS;

BACTERIOLYSIS; BACTERIOPHAGE; DISEASE TRANSMISSION; ENDEMIC DISEASE; EPIDEMIC; GROWTH CURVE; INFECTION RATE; MARINE ENVIRONMENT; MATHEMATICAL ANALYSIS; NONHUMAN; OSCILLATION; POPULATION DYNAMICS; REVIEW; VIRUS REPLICATION;

BACTERIA (MICROORGANISMS);

EID: 0031802262     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(97)10015-3     Document Type: Article

References (13)

1. Proctor L.M., Fuhrman J.A. Viral mortality of marine bacteria and cyanobacteria. Nature. 343:1990;60.
2. Moebus K. Lytic and inhibition responses to bacteriophages among marine bacteria, with special reference to the origin of phage-host systems. Helgolander Meeresuntersuchungen. 36:1983;375.
3. J. Sieburth, Sea Microbes, Oxford University, New York, 1979.
4. Bergh O., Borsheim K.Y., Bratbak G., Heldal M. High abundance of viruses found in aquatic environments. Nature. 340:1989;467.
5. Anderson R.M., May R.M. The population dynamics of microparasites and their invertebrate hosts. Proc. Roy. Soc. Lond. B. 291:1981;451.
6. Levin B. Frequency-dependent selection in bacterial populations. Phil. Trans. Roy. Soc. Lond. B. 319:1988;459.
7. Pugliese A. Population models for diseases with no recovery. J. Math. Biol. 28:1990;65.
8. Nagumo N. Uber die Lage der Integralkurven gewonlicher Differantialgleichungen. Proc. Phys. Math. Soc. Japan. 24:1942;551.
9. Barbǎlat I. Systemes d'equations differentielles d'oscillation non lineares. Rev. Math. Pure et Appl. 4:1959;267.
10. Liu W.M. Criterion of Hopf bifurcations without using eigenvalues. J. Math. Anal. Appl. 182:1994;250.
11. Thieme H.R. Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24:1993;407.
12. K. Cooke, Y. Kuang, B. Li, Analysis of an antiviral immune response model with time delays, Proceedings of the Third Butler conference (submitted).
13. G.B. Ermentrout, XPPAUT 3.0, the differential equation tool, http://info.pitt.edu/phase/, 1997.