Epidemic Thresholds and Vaccination in a Lattice Model of Disease Spread

Anderson, 1991 Anderson, 1981, Population dynamics of fox rabies in Europe, Nature (Lond.), 289, 765, 10.1038/289765a0 Bailey, 1975 Bartlett, 1960, The critical community size for measles in the U.S, J. R. Statist. Soc. A, 123, 37, 10.2307/2343186 Black, 1966, Measles endemicity in insular populations: Critical community size and its evolutionary implications, J. Theo. Biol., 11, 207, 10.1016/0022-5193(66)90161-5 Boccara, 1992, Automata network models for the spread of infectious diseases in a population of moving individuals, J. Phys. A, 25, 2447, 10.1088/0305-4470/25/9/018 Bolker, 1995, Space, persistence and dynamics of measles epidemics, Phil. Trans. R. Soc. (Lond.), 348, 309, 10.1098/rstb.1995.0070 Cox, 1988, Limit theorems for the spread of epidemics and forest fires, Stoc. Proc. Applics., 30, 171, 10.1016/0304-4149(88)90083-X Durrett, 1995, Spatial epidemic models Durrett, 1994, Particle systems and reaction- diffusion equations, Ann. Probab., 22, 289, 10.1214/aop/1176988861 Durrett, 1991, Epidemics with recovery ind, Ann. Appl. Prob., 1, 189, 10.1214/aoap/1177005933 Durrett, 1994, The importance of being discrete (and spatial), Theor. Popul. Biol., 46, 363, 10.1006/tpbi.1994.1032 Durrett, 1994, Stochastic spatial models: a user's guide to ecological applications, Phil. Trans. R. Soc. (Lond.) B, 343, 329, 10.1098/rstb.1994.0028 Grenfell, 1992, Chance and chaos in measles dynamics, J. R. Statist. Soc. B, 54, 383 Hassell, 1991, Spatial structure and chaos in insect population dynamics, Nature (Lond.), 353, 255, 10.1038/353255a0 Johansen, 1994, Spatio-temporal self-organisation in a model of disease spreading, Physica D, 78, 186, 10.1016/0167-2789(94)90114-7 Johansen, 1966, A simple model of recurrent epidemics, J. Theo. Biol., 178, 45, 10.1006/jtbi.1996.0005 May, 1984, Spatial heterogeneity and the design of immunisation programs, Math. Biosci., 76, 1 May, 1992, Evolutionary games and spatial chaos, Nature (Lond.), 359, 826, 10.1038/359826a0 Mollison, 1977, Spatial contact models for ecological and epidemic spread,, J. R. Statist. Soc. B, 39, 283 Mollison, 1991, Dependence of epidemic and population velocities on basic parameters, Math. Biosci., 107, 255, 10.1016/0025-5564(91)90009-8 Murray, 1986, On the spatial spread of rabies among foxes, Proc. Roy. Soc. (Lond.) B, 229, 111, 10.1098/rspb.1986.0078 Noble, 1974, Geographic and temporal development of plagues, Nature (Lond.), 250, 726, 10.1038/250726a0 Olsen, 1990, Chaos versus noisy periodicity: Alternative hypotheses for childhood epidemics, Science (Wash.), 249, 499, 10.1126/science.2382131 Olsen, 1988, Oscillations and chaos in epidemics: A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark, Theo. Popul. Biol., 33, 344, 10.1016/0040-5809(88)90019-6 Pacala, 1990, Host-parasitoid associations in patchy environments, Nature (Lond.), 344, 150, 10.1038/344150a0 Rand, 1995, Invasion stability and evolution to criticality in spatially extended, artificial host-pathogen ecologies, Proc. Roy. Soc. (Lond.) B, 259, 55, 10.1098/rspb.1995.0009 Rhodes, 1996, Dynamics in a lattice epidemic model, Phys. Lett. A, 210, 183, 10.1016/S0375-9601(96)80007-7 Rhodes, 1966, Persistence and dynamics in lattice models of epidemic spread, J. Theor. Biol. Rhodes, 1996, Power laws governing epidemics in isolated populations, Nature (Lond.), 381, 600, 10.1038/381600a0 Schenzle, 1984, An age-structured model of pre- and post-vaccination massles transmission, IMA J. Math. Appl. Med. Biol., 1, 169, 10.1093/imammb/1.2.169 Schonfisch, 1995, Propagation of fronts in cellular automata, Physica D, 80, 433, 10.1016/0167-2789(94)00192-S Smith, 1991, Rabies in urban foxes (Vulpes vulpes, Proc. Roy. Soc. (Lond.) B, 334, 459 Viswanathan, 1996, Levy flight search patterns of wandering albatrosses, Nature (Lond.), 381, 413, 10.1038/381413a0