Oscillations and waves in a virally infected plankton system: Part II: Transition from lysogeny to lysis

A model of phytoplankton–zooplankton prey–predator dynamics is considered for the case of viral infection of the phytoplankton population. 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) as a Holling-type II predator is grazing on susceptibles and infected. The local and spatial analyses of the S–I–Z model with lysogenic infection have been presented in a previous paper (Malchow et al., 2004b. Oscillations and waves in a virally infected plankton system: Part I: The lysogenic stage. Ecol. Complexity 1 (3), 211–223). This lysogenic stage is rather sensitive to environmental variability. Therefore, the effect of a transition from lysogeny to lysis is investigated here. The replication rate of the infected species instantaneously falls to zero. A deterministic and a more realistic stochastic scenario are described. The spatiotemporal behaviour, modelled by deterministic and stochastic reaction-diffusion equations, is numerically determined. It is shown that the extinction risk of the infected is rather high in the deterministic system, whereas the environmental noise enhances their chance of spatial spread and survival.