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Epidemic thresholds and vaccination in a lattice model of disease spread. (English) Zbl 0886.92027
Summary: 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 an 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.

MSC:
92D30 Epidemiology
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