A conceptual prey-predator model of phytoplankton-zooplankton dynamics [1,2,3] is considered for the case of viral infection of the phytoplankton population. There is not so much known about the mechanisms of viral infection and spread of disease in and between plankton populations. A few papers on the modelling of the impact of lytic [4,5] and lysogenic [6] virus infections on plankton communities have been published. Here, the phytoplankton population is split into a susceptible (S) and an infected (I) part. Both parts grow logistically, limited by a common carrying capacity. Zooplankton (Z) is grazing on susceptibles and infected. The local analysis of the S-I-Z differential equations yields a number of stationary and/or oscillatory regimes and their combinations. Correspondingly interesting is the spatiotemporal behaviour, modelled by reaction-diffusion equations. Spatial spread or suppression of infection will be presented just as well as competition of concentric and/or spiral population waves with non-oscillatory sub-populations for space, and long transients to spatially homogeneous population distributions.
Bibliography
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3. H. Malchow. Spatio-temporal pattern formation in nonlinear nonequilibrium plankton dynamics. Proc. R. Soc. Lond. B, 251:103-109, 1993.
4. E. Beltrami and T.O. Carroll. Modelling the role of viral disease in recurrent phytoplankton blooms. J. Math. Biol., 32:857-863, 1994.
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