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Dynamics of a virus-host model with an intrinsic quota. (English) Zbl 1217.37080

Summary: We develop and analyze a mathematical model describing the dynamics of infection by a virus of a host population in a freshwater environment. Our model, which consists of a system of nonlinear ordinary differential equations, includes an intrinsic quota, that is, we use a nutrient (e.g., phosphorus) as a limiting element for the host and potentially for the virus. Motivation for such a model arises from studies that raise the possibility that on the one hand, viruses may be limited by phosphorus, and on the other, that they may have a role in stimulating the host to acquire the nutrient. We perform an in-depth mathematical analysis of the system including the existence and uniqueness of solutions, equilibria, asymptotic, and persistence analysis. We compare the model with experimental data, and find that biologically meaningful parameter values provide a good fit. We conclude that the mathematical model supports the hypothesized role of stored nutrient regulating the dynamics, and that the coexistence of virus and host is the natural state of the system.

MSC:

37N25 Dynamical systems in biology
92D30 Epidemiology
34D20 Stability of solutions to ordinary differential equations
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[1] Pomeroy, L.R., Oceans food web, a changing paradigm, Bioscience, 24, 499-504, (1974)
[2] Azam, F.; Fenchel, T.; Field, J.G.; Gray, J.S.; Meyer Reil, L.A.; Thingstad, F., The ecological role of water-column microbes in the sea, Marine ecology progress series, 10, 257-263, (1983)
[3] Fuhrman, J., Marine viruses and their biogeochemical and ecological effects, Nature, 399, 541-548, (1999)
[4] Gons, H.J.; Hoogveld, H.L.; Simis, S.G.H.; Tijdens, M., Dynamic modelling of viral impact on cyanobacterial populations in shallow lakes: implications of burst size, Journal of the marine biological association of the united kingdom, 86, 537-542, (2006)
[5] Middelboe, M., Bacterial growth rate and marine virus – host dynamics, Microbial ecology, 40, 114-124, (2000)
[6] Middelboe, M.; Hagström, A.; Blackburn, N.; Sinn, B.; Fisher, U.; Borch, N.H.; Pinhassi, J.; Simu, K.; Lorenz, M.G., Effects of bacteriophages on the population dynamics of four strains of pelagic marine bacteria, Microbial ecology, 42, 395-406, (2001)
[7] Thingstad, T.F.; Heldal, M.; Bratbak, G.; Dundas, I., Are viruses important partners in pelagic food webs?, Trends in ecology & evolution, 8, 209-213, (1993)
[8] Weinbauer, M.; Rassoulzadegan, F., Are viruses driving microbial diversification and diversity?, Environmental microbiology, 6, 1-11, (2004)
[9] Wilson, W.H.; Mann, N.H., Lysogenic and lytic viral production in microbial communities, Aquatic microbial ecology, 13, 95-100, (2007)
[10] Murray, A.G.; Jackson, G.A., Viral dynamics: a model of the effect of size, shape, motion and abundance of single-celled planktonic organisms and other particles, Marine ecology progress series, 89, 103-116, (1992)
[11] Proctor, L.M.; Fuhrman, J.A., Viral mortality of marine bacteria and cyanobacteria, Nature, 343, 60-62, (1990)
[12] Beretta, E.; Kuang, Y., Modeling and analysis of a marine bacteriophage infection, Mathematical biosciences, 149, 57-76, (1998) · Zbl 0946.92012
[13] Middelboe, M.; Jørgensen, M.; Kroer, N., Effects of viruses on nutrient turnover and growth efficiency on noninfected marine bacterioplankton, Applied and environmental microbiology, 62, 1991-1997, (1996)
[14] Cunningham, A.; Nisbet, R., Transient oscillation in continuous culture, (), 77-103, (Chapter 3)
[15] Droop, M.R., The nutrient status of algal cells in continuous culture, Journal of the marine biological association of the united kingdom, 54, 825-855, (1974)
[16] Fu, F.; Zhang, Y.; Bell, P.; Hutchins, D., Phosphate uptake and growth kinetics of trichodesmium (cyanobacteria) isolates from the north atlantic Ocean and the great barrier reef, Australia, Journal of phycology, 41, 62-73, (2005)
[17] Bratbak, G.; Egge, J.K.; Heldal, M., Viral mortality of the marine alga emiliania huxleyi (haptophyceae) and termination of algal blooms, Marine ecology progress series, 93, 39-48, (1993)
[18] W.H. Wilson, Functional genomics acquisition during virus infection of Emiliania huxleyi, NSF Award # 0723730 Project Summary.
[19] Edwards, A.M., Adding detritus to a nutrient – phytoplankton – zooplankton model: a dynamical-systems approach, Journal of plankton research, 23, 389-413, (2001)
[20] Edwards, A.M.; Brindley, J., Oscillatory behaviour in a three-component plankton population model, Dynamics and stability of systems, 11, 347-370, (1996) · Zbl 0871.92029
[21] Jang, S.R.-J., Dynamics of variable-yield nutrient – phytoplankton – zooplankton models with nutrient recycling and self-shading, Journal of mathematical biology, 40, 229-250, (2000) · Zbl 0998.92039
[22] Ikeya, T.; Ohki, K.; Takahashi, M.; Fujita, Y., Study of phosphate uptake of the marine cyanophyte synechococcus sp. NIBB 1071 in relation to oligotrophic environments in the open Ocean, Marine biology, 129, 195-202, (1997)
[23] Wilson, W.H.; Schroeder, D.C.; Allen, M.J.; Holden, M.T.; Parkhill, J.; Barrell, B.G.; Churcher, C.; Hamlin, N.; Mungall, K.; Norbertczak, H.; Quail, M.A.; Price, C.; Rabbinowitsch, E.; Walker, D.; Craigon, M.; Roy, D.; Ghazal, P., Complete genome sequence and lytic phase transcription profile of a coccolithovirus, Science, 309, 1090-1092, (2005)
[24] Lean, D.R.S.; Cuhel, R.L., Subcellular phosphorus kinetics for lake Ontario plankton, Canadian journal of fisheries and aquatic sciences, 44, 2077-2086, (1987)
[25] Freedman, H.I.; Waltman, P., Persistence in models of three interacting predator – prey populations, Mathematical biosciences, 68, 213-231, (1984) · Zbl 0534.92026
[26] Bertilsson, S.; Berglund, O.; Karl, D.M.; Chisholm, S.W., Elemental composition of marine prochlorococcus and synechococcus: implications for the ecological stoichiometry of the sea, Limnology and oceanography, 48, 1721-1731, (2003)
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