Spatial Contact Models for Ecological and Epidemic Spread

[1]  A. W. Davis On the theory of birth, death and diffusion processes , 1965, Journal of Applied Probability.

[2]  D. Downham,et al.  Inference for a two-dimensional stochastic growth model , 1976 .

[3]  D. Aronson,et al.  Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation , 1975 .

[4]  J. Hammersley Postulates for Subadditive Processes , 1974 .

[5]  D. Vere-Jones On Updating Algorithms and Inference for Stochastic Point Processes , 1975, Journal of Applied Probability.

[6]  T. Williams,et al.  Stochastic Model for Abnormal Clone Spread through Epithelial Basal Layer , 1972, Nature.

[7]  E. Renshaw Stepping stone models for population growth , 1974, Journal of Applied Probability.

[8]  D. Mollison,et al.  Conjecture on the Spread of Infection in Two Dimensions Disproved , 1972, Nature.

[9]  M. Bartlett Measles Periodicity and Community Size , 1957 .

[10]  H. Daniels Saddlepoint Approximations in Statistics , 1954 .

[11]  G. Wickens Speculations on Long Distance Dispersal and the Flora of Jebel Marra, Sudan Republic , 1976 .

[12]  Norman T. J. Bailey,et al.  The simulation of stochastic epidemics in two dimensions , 1967 .

[13]  O. Kallenberg Canonical representations and convergence criteria for processes with interchangeable increments , 1973 .

[14]  E. Montroll On nonlinear processes involving population growth and diffusion , 1967, Journal of Applied Probability.

[15]  Peter J. Diggle A spatial stochastic model of inter-plant competition , 1976 .

[16]  W. Fleming DIFFUSION PROCESSES IN POPULATION BIOLOGY , 1975 .

[17]  Frank Kelly,et al.  The asymptotic behaviour of an invasion process , 1977, Journal of Applied Probability.

[18]  J. McLeod,et al.  The approach of solutions of nonlinear diffusion equations to travelling wave solutions , 1975 .

[19]  Klaus Dietz,et al.  Epidemics and Rumours: A Survey , 1967 .

[20]  D. Downham,et al.  Growth of Abnormal Cells , 1973, Nature.

[21]  José Canosa,et al.  NUMERICAL SOLUTION OF FISHER'S EQUATION , 1974 .

[22]  Andrew D. Barbour,et al.  Quasi–stationary distributions in Markov population processes , 1976, Advances in Applied Probability.

[23]  Aidan Sudbury The size of the region occupied by one type in an invasion process , 1976, Journal of Applied Probability.

[24]  J. Radcliffe The convergence of a position-dependent branching process used as an approximation to a model describing the spread of an epidemic , 1976, Journal of Applied Probability.

[25]  D. Welsh,et al.  A Two‐Dimensional Poisson Growth Process , 1965 .

[26]  N. Jardine,et al.  Continental Drift and the Dispersal and Evolution of Organisms , 1972, Nature.

[27]  J. Kingman The First Birth Problem for an Age-dependent Branching Process , 1975 .

[28]  R. Fisher THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[29]  D. Mollison Spatial propagation of simple epidemics , 1971 .

[30]  Denis Mollison,et al.  The Velocity of Stochastic Processes , 1977 .

[31]  A. Barbour The uniqueness of Atkinson and Reuter's epidemic waves , 1977, Mathematical Proceedings of the Cambridge Philosophical Society.

[32]  José Canosa,et al.  On a nonlinear diffusion equation describing population growth , 1973 .

[33]  C. Preston Spatial birth and death processes , 1975, Advances in Applied Probability.

[34]  Frank Hoppenstaedt Mathematical Theories of Populations: Demographics, Genetics and Epidemics , 1975 .

[35]  M. Bartlett,et al.  Stochastic Population Models in Ecology and Epidemiology. , 1961 .

[36]  R. Howell Dutch Elm disease data , 1975, Advances in Applied Probability.

[37]  E. C. Stakman,et al.  Principles of plant pathology. , 1957 .

[38]  A form of wave propagation associated with the equation of heat conduction , 1948 .

[39]  N. Ling The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[40]  H. McKean Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov , 1975 .

[41]  J. G. Skellam Random dispersal in theoretical populations , 1951, Biometrika.

[42]  M. J. Faddy,et al.  Stochastic compartmental models as approximations to more general stochastic systems with the general stochastic epidemic as an example , 1977, Advances in Applied Probability.

[43]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[44]  D. Mollison Percolation processes and tumour growth , 1974, Advances in Applied Probability.

[45]  P. B. Wright EFFECTS OF WIND AND PRECIPITATION ON THE SPREAD OF FOOT-AND-MOUTH DISEASE , 1969 .

[46]  M. S. Bartlett,et al.  Processus stochastiques ponctuels , 1954 .

[47]  E. D. Ford,et al.  Competition and stand structure in some even-aged plant monocultures , 1975 .

[48]  J. Biggins Asymptotic properties of the branching random walk , 1976 .

[49]  G. Reuter,et al.  Deterministic epidemic waves , 1976, Mathematical Proceedings of the Cambridge Philosophical Society.

[50]  Robin Sibson,et al.  Computing Dirichlet Tessellations in the Plane , 1978, Comput. J..

[51]  J. M. Hammersley,et al.  First‐Passage Percolation , 1966 .

[52]  A. Ammerman,et al.  A population model for the diffusion of early farming in Europe , 1973 .

[53]  P. Clifford,et al.  A model for spatial conflict , 1973 .

[54]  Mark Bartlett,et al.  Deterministic and Stochastic Models for Recurrent Epidemics , 1956 .

[55]  Yoshinori Kametaka,et al.  On the nonlinear diffusion equation of Kolmogorov-Petrovskii-Piskunov type , 1975 .

[56]  Denis Mollison,et al.  Possible velocities for a simple epidemic , 1972, Advances in Applied Probability.

[57]  J. Kingman Subadditive Ergodic Theory , 1973 .

[58]  H. Daniels The Deterministic Spread of a Simple Epidemic , 1975, Journal of Applied Probability.

[59]  M. Eden A Two-dimensional Growth Process , 1961 .

[60]  Denis Mollison,et al.  Markovian contact processes , 1978, Advances in Applied Probability.

[61]  D. Richardson Random growth in a tessellation , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[62]  T. E. Harris A lower bound for the critical probability in a certain percolation process , 1960, Mathematical Proceedings of the Cambridge Philosophical Society.

[63]  J. Kingman,et al.  The Ergodic Theory of Subadditive Stochastic Processes , 1968 .

[64]  R. Lorenz,et al.  Ein Modell der Plaquebildung , 1966 .

[65]  Denis Mollison,et al.  The rate of spatial propagation of simple epidemics , 1972 .

[66]  Stanley Sawyer,et al.  Branching diffusion processes in population genetics , 1976, Advances in Applied Probability.

[67]  R. Smythe Remarks on renewal theory for percolation processes , 1976, Journal of Applied Probability.

[68]  N. Bailey Stochastic birth, death and migration processes for spatially distribured populations. , 1968, Biometrika.

[69]  T. E. Harris Contact Interactions on a Lattice , 1974 .

[70]  G. H. Markstein Theory of Flame Propagation , 1964 .

[71]  J. Hammersley,et al.  First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theory , 1965 .

[72]  H. Daniels Approximate Solutions of Green's Type for Univariate Stochastic Processes , 1960 .

[73]  M. Bartlett The statistical analysis of spatial pattern , 1974, Advances in Applied Probability.

[74]  S. Rushton,et al.  THE DETERMINISTIC MODEL OF A SIMPLE EPIDEMIC FOR MORE THAN ONE COMMUNITY , 1955 .

[75]  J. Radcliffe The initial geographical spread of host-vector and carrier-borne epidemics , 1973, Journal of Applied Probability.

[76]  J. Carr,et al.  Deterministic epidemic waves of critical velocity , 1977, Mathematical Proceedings of the Cambridge Philosophical Society.

[77]  H. E. Daniels,et al.  The advancing wave in a spatial birth process , 1977, Advances in Applied Probability.

[78]  J. D. Biggins,et al.  The asymptotic shape of the branching random walk , 1978, Advances in Applied Probability.

[79]  D. A. Larson Transient Bounds and Time-Asymptotic Behavior of Solutions to Nonlinear Equations of Fisher Type , 1978 .