Laboratory experiments with whole water-columns from shallow, eutrophic lakes repeatedly showed collapse of the predominant filamentous cyanobacteria. The collapse could be due to viral activity, from the evidence of electron microscopy of infected cyanobacterial cells and observed dynamics of virus-like particles. Burst-size effects on single-host single-virus dynamics was modelled for nutrient-replete growth of the cyanobacteria and fixed viral decay rate in the water column. The model combined previously published equations for nutrient-replete cyanobacterial growth and virus–host relationship. According to the model results, burst sizes greater than 200 to 400 virions per cell would result in host extinction, whereas lower numbers would allow coexistence, and even stable population densities of host and virus. High-nutrient status of the host cells might accommodate a large burst size. The ecological implication could be that burst-size increase accompanying a transition from phosphorus to light-limited cyanobacterial growth might destabilize the virus–host interaction and result in the population collapse observed in the experiments.