Epidemic Thresholds and Vaccination in a Lattice Model of Disease Spread

We use a lattice-based epidemic model to study the spatial and temporal rates of disease spread in a spatially distributed host population. The prevalence of the disease in the population is studied as well as the spread of infection about a point source of infection. In particular, two distinct critical population densities are identified. The first relates to the minimum population density for a epidemic to occur, whilst the second is the minimum population density for long-term persistence to occur. Vaccination regimes are introduced that are used to measure the impact of spatially and nonspatially dependent intervention strategies. Specifically we show how a ring of vaccinated susceptibles, of sufficient thickness, can halt the spread of infection across space.