title: Epidemic thresholds and vaccination in a lattice model of disease spread.
abstract: 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.
authors.affiliation: Centre for the Epidemiology of Infectious Disease, Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, United Kingdom.
authors.forename: C J
authors.initials: CJ
authors.lastname: Rhodes
authors.forename: R M
authors.initials: RM
authors.lastname: Anderson
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D019353:Endemic Diseases; D006801:Humans; D015233:Models, Statistical; D011156:Population Density; D015995:Prevalence; D015203:Reproducibility of Results; D013029:Space-Time Clustering; D013269:Stochastic Processes; D013997:Time Factors; D014611:Vaccination