论文信息 - Epidemic Models, Spatial

Epidemic Models, Spatial

For a proper understanding of the dispersal and control of infectious diseases, it is often necessary to consider spatial models in which individuals do not mix homogeneously. A birth, death, and migration/infection process for separate colonies, with migration/infection to nearest neighboring colonies, is considered from both deterministic and stochastic viewpoint. Topics covered include Monte Carlo simulation and threshold levels, with particular reference to the transmission of HIV/AIDS and rabies. Keywords: contact distribution; birth–death–migration process; Brownian motion; reproduction number; Monte Carlo simulation; thresholds; Turing ring; HIV/AIDS; rabies

Eric Renshaw | E. Renshaw

[1] Valerie Isham,et al. Mathematical modelling of the transmission dynamics of HIV infection and AIDS (a review) , 1988 .

[2] D Mollison,et al. Dependence of epidemic and population velocities on basic parameters. , 1991, Mathematical biosciences.

[3] D Mollison,et al. Epidemics: models and data. , 1994, Journal of the Royal Statistical Society. Series A,.

[4] A. Turing. The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

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

[6] E. Renshaw,et al. Gibbs point processes for studying the development of spatial-temporal stochastic processes , 2001 .

[7] Ecology of Infectious Diseases in Natural Populations: Spatial Dynamics Group Report , 1995 .

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

[9] E. Renshaw. Velocities of propagation for stepping-stone models of population growth , 1977, Journal of Applied Probability.

[10] Rick Durrett,et al. Limit theorems for the spread of epidemics and forest fires , 1988 .

[11] E. Renshaw,et al. The Interpretation of Process from Pattern Using Two‐Dimensional Spectral Analysis: Methods and Problems of Interpretation , 1983 .

[12] E. Renshaw,et al. Applying the saddlepoint approximation to bivariate stochastic processes. , 2000, Mathematical biosciences.