Persistence and dynamics in lattice models of epidemic spread

被引:53
作者
Rhodes, CJ
Anderson, RM
机构
[1] Department of Zoology, University of Oxford, Oxford, OX1 3PS, South Parks Road
基金
英国惠康基金;
关键词
D O I
10.1006/jtbi.1996.0088
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
We present a simple epidemic model representing the spread of a communicable disease in a spatially extended host population. The model falls into the general class of techniques which utilise lattice based simulation as a way of incorporating spatial effects. The factors relating to the persistence and dynamics of the disease are investigated. There exists a clear population threshold below which the disease dies out and above which it settles to an endemically stable state. The rate of population mixing is shown to affect this threshold density. Equations which accurately account for the mean-field limit of the model are introduced and the relevance to the epidemiological modelling of measles is discussed. (C) 1996 Academic Press Limited
引用
收藏
页码:125 / 133
页数:9
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共 23 条
[11]  
DIETZ K, 1985, J MATH BIOL, V22, P117
[12]   STOCHASTIC SPATIAL MODELS - A USERS GUIDE TO ECOLOGICAL APPLICATIONS [J].
DURRETT, R ;
LEVIN, SA .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES B-BIOLOGICAL SCIENCES, 1994, 343 (1305) :329-350
[13]   MEASLES IN ENGLAND AND WALES .1. AN ANALYSIS OF FACTORS UNDERLYING SEASONAL PATTERNS [J].
FINE, PEM ;
CLARKSON, JA .
INTERNATIONAL JOURNAL OF EPIDEMIOLOGY, 1982, 11 (01) :5-14
[14]   ON THE CRITICAL-BEHAVIOR OF THE GENERAL EPIDEMIC PROCESS AND DYNAMICAL PERCOLATION [J].
GRASSBERGER, P .
MATHEMATICAL BIOSCIENCES, 1983, 63 (02) :157-172
[15]  
GRENFELL BT, 1992, J ROY STAT SOC B MET, V54, P383
[16]   SPATIAL STRUCTURE AND CHAOS IN INSECT POPULATION-DYNAMICS [J].
HASSELL, MP ;
COMINS, HN ;
MAY, RM .
NATURE, 1991, 353 (6341) :255-258
[17]   RECURRENT OUTBREAKS OF MEASLES, CHICKENPOX AND MUMPS .1. SEASONAL-VARIATION IN CONTACT RATES [J].
LONDON, WP ;
YORKE, JA .
AMERICAN JOURNAL OF EPIDEMIOLOGY, 1973, 98 (06) :453-468
[18]   OSCILLATIONS AND CHAOS IN EPIDEMICS - A NONLINEAR DYNAMIC STUDY OF 6 CHILDHOOD DISEASES IN COPENHAGEN, DENMARK [J].
OLSEN, LF ;
TRUTY, GL ;
SCHAFFER, WM .
THEORETICAL POPULATION BIOLOGY, 1988, 33 (03) :344-370
[19]   CHAOS VERSUS NOISY PERIODICITY - ALTERNATIVE HYPOTHESES FOR CHILDHOOD EPIDEMICS [J].
OLSEN, LF ;
SCHAFFER, WM .
SCIENCE, 1990, 249 (4968) :499-504
[20]   HOST PARASITOID ASSOCIATIONS IN PATCHY ENVIRONMENTS [J].
PACALA, SW ;
HASSELL, MP ;
MAY, RM .
NATURE, 1990, 344 (6262) :150-153