Well-established theoretical models predict host density thresholds for invasion and persistence of parasites with a density-dependent transmission. Studying such thresholds in reality, however, is not obvious because it requires long-term data for several fluctuating populations of different size. We developed a spatially explicit and individual-based SEIR model of Mopeia virus in multimammate mice Mastomys natalensis. This is an interesting model system for studying abundance thresholds because the host is the most common African rodent, populations fluctuate considerably and the virus is closely related to Lassa virus but non-pathogenic to humans so can be studied safely in the field. The simulations show that, while host density clearly is important, sharp thresholds are only to be expected for persistence (and not for invasion), since at short time-spans (as during invasion), stochasticity is determining. Besides host density, also the spatial extent of the host population is important. We observe the repeated local occurrence of herd immunity, leading to a decrease in transmission of the virus, while even a limited amount of dispersal can have a strong influence in spreading and re-igniting the transmission. The model is most sensitive to the duration of the infectious stage, the size of the home range and the transmission coefficient, so these are important factors to determine experimentally in the future.
Journal of Theoretical Biology, 2013, Vol 317, p. 55-61