Spatial models in the epidemiology of infectious diseases

We shall concentrate in this review on the population dynamics of infectious diseases, with special emphasis on the explicit handling of spatial components. Even the simplest nonspatial infectious disease models are moderately complex. The Law of Mass Action is used to describe the rate at which new infections occur in a community, i.e. making it proportional to the product of the numbers of both susceptible and infectious persons existing at any particular time. This makes the process nonlinear.

[1]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[2]  J. Gani,et al.  Perspectives in Probability and Statistics. , 1980 .

[3]  J. Wierman.  The front velocity of the simple epidemic , 1979, Journal of Applied Probability.

[4]  Horst R. Thieme,et al.  Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations. , 1979 .

[5]  O. Diekmann,et al.  Thresholds and travelling waves for the geographical spread of infection , 1978, Journal of mathematical biology.

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

[7]  N. Mcglashan.  Viral hepatitis in Tasmania. , 1977, Social science & medicine.

[8]  H. Thieme.  A model for the spatial spread of an epidemic , 1977, Journal of mathematical biology.

[9]  I. Gertsbakh.  Epidemic process on a random graph: some preliminary results , 1977, Journal of Applied Probability.

[10]  Denis Mollison,et al.  Spatial Contact Models for Ecological and Epidemic Spread , 1977 .

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

[12]  J. Radcliffe.  The severity of a viral host-vector epidemic , 1976, Journal of Applied Probability.

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

[14]  L. Billard.  A stochastic general epidemic in m sub-populations , 1976, Journal of Applied Probability.

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

[16]  M. Hugh-jones,et al.  A simulation spatial model of the spread of foot-and-mouth disease through the primary movement of milk , 1976, Journal of Hygiene.

[17]  A. D. Cliff,et al.  Model Building and the Analysis of Spatial Pattern in Human Geography , 1975 .

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

[19]  Noble Jv,et al.  Geographic and temporal development of plagues , 1974 .

[20]  M. Splaine,et al.  On the use of contour maps in the analysis of spread of communicable disease , 1974, Journal of Hygiene.

[21]  D. Kelker.  A Random Walk Epidemic Simulation , 1973 .

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

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

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

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

[26]  R. Kryscio.  The transition probabilities of the extended simple stochastic epidemic model and the Haskey model , 1972, Journal of Applied Probability.

[27]  Donald R. MoNEIL.  On the simple stochastic epidemic , 1972 .

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

[29]  R. Watson,et al.  On an epidemic in a stratified population , 1972, Journal of Applied Probability.

[30]  Rvachev La.  Modelling of medicobiological processes in society as a class of continuum dynamics , 1972 .

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

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

[33]  T. Williams,et al.  Hyperplasia: The spread of abnormal cells through a plane lattice , 1971, Advances in Applied Probability.

[34]  R. Tinline.  Lee Wave Hypothesis for the Initial Pattern of Spread during the 1967-68 Foot and Mouth Epizootic , 1970, Nature.

[35]  N. C. Severo.  A recursion theorem on solving differential-difference equations and applications to some stochastic processes , 1969, Journal of Applied Probability.

[36]  N. G. Becker.  The spread of an epidemic to fixed groups within the population. , 1968, Biometrics.

[37]  N. C. Severo.  Two theorems on solutions of differential-difference equations and applications to epidemic theory , 1967, Journal of Applied Probability.

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

[39]  Josiah Macy,et al.  Mathematics and Computer Science in Biology and Medicine , 1966 .

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

[41]  J. Hunter.  River Blindness in Nangodi, Northern Ghana: A Hypothesis of Cyclical Advance and Retreat , 1966 .

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

[43]  J. Gurland,et al.  Stochastic Models in Medicine and Biology , 1964 .

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

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

[46]  H. W. Haskey.  STOCHASTIC CROSS-INFECTION BETWEEN TWO OTHERWISE ISOLATED GROUPS , 1957 .

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

[48]  Edwin B. Wilson,et al.  The Spread of an Epidemic. , 1945, Proceedings of the National Academy of Sciences of the United States of America.

[49]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[50]  C. Spicer.  The mathematical modelling of influenza epidemics. , 1979, British medical bulletin.

[51]  J F Boisvieux,et al.  [Mathematical model of the propagation of a vulpine rabies epizootic (author's transl)]. , 1978, Revue d'epidemiologie et de sante publique.

[52]  B. Ripley.  Modelling Spatial Patterns , 1977 .

[53]  B. Sayers,et al.  A pattern-analysis study of a wild-life rabies epizootic , 1977 .

[54]  K Dietz,et al.  Characteristics of the spread of a wildlife rabies epidemic in Europe. , 1976, Bulletin of the World Health Organization.

[55]  K. Dietz,et al.  The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations , 1976 .

[56]  J. Berger.  Model of Rabies Control , 1976 .

[57]  Norman T. J. Bailey,et al.  The Mathematical Theory of Infectious Diseases , 1975 .

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

[59]  Rvachev La.  Experiment in machine prognostication of an influenza epidemic , 1971 .

[60]  L. A. Rvachev,et al.  Computer modelling of influenza epidemics for the whole country (USSR) , 1971, Advances in Applied Probability.

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

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

[63]  M. S. Bartlett,et al.  Monte Carlo Studies in Ecology and Epidemiology , 1961 .

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

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

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

[67]  H. E. Soper.  The Interpretation of Periodicity in Disease Prevalence , 1929 .