A PROBABILISTIC-AUTOMATA NETWORK EPIDEMIC MODEL WITH BIRTHS AND DEATHS EXHIBITING CYCLIC BEHAVIOR

被引:53
作者
BOCCARA, N [1 ]
CHEONG, KO [1 ]
ORAM, M [1 ]
机构
[1] UNIV ILLINOIS, DEPT PHYS, CHICAGO, IL 60607 USA
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1994年 / 27卷 / 05期
关键词
D O I
10.1088/0305-4470/27/5/022
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A probabilistic automata network model for the spread of an infectious disease in a population of moving individuals is studied. The local rule consists of two subrules. The first one, applied synchronously, models infection, birth and death processes. It is a probabilistic cellular automaton rule. The second, applied sequentially, describes the motion of the individuals. The model contains six parameters: the probabilities p for a susceptible to become infected by contact with an infective; the respective birth rates b(s) and b(i) of the susceptibles from either a susceptible or an infective parent; the respective death rates d(s) and d(i) of susceptibles and infectives; and a parameter in characterizing the motion of the individuals. The model has three fixed points. The first is trivial, it describes a stationary state with no living individuals. The second corresponds to a disease-free state with no infectives. The third and last one characterizes an endemic state with non-zero densities of susceptibles and infectives. Moreover, the model may exhibit oscillatory behaviour of the susceptible and infective densities as functions of time through a Hopf-type bifurcation. The influence of the different parameters on the stability of all these states is studied with a particular emphasis on the influence of motion which has been found to be a stabilizing factor of the cyclic behaviour.
引用
收藏
页码:1585 / 1597
页数:13
相关论文
共 10 条
[1]  
ANDERSON R M, 1991
[2]  
[Anonymous], 1975, MATH THEORY INFECT D
[3]  
BEASE J, 1977, J PHYS C SOLID STATE, V10, P917
[4]   CRITICAL-BEHAVIOR OF A PROBABILISTIC-AUTOMATA NETWORK SIS MODEL FOR THE SPREAD OF AN INFECTIOUS-DISEASE IN A POPULATION OF MOVING INDIVIDUALS [J].
BOCCARA, N ;
CHEONG, K .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (15) :3707-3717
[5]  
BOCCARA N, 1992, J PHYS A, V25, P1
[6]   COLLECTIVE BEHAVIORS IN SPATIALLY EXTENDED SYSTEMS WITH LOCAL INTERACTIONS AND SYNCHRONOUS UPDATING [J].
CHATE, H ;
MANNEVILLE, P .
PROGRESS OF THEORETICAL PHYSICS, 1992, 87 (01) :1-60
[7]  
Goles E., 1990, NEURAL AUTOMATA NETW
[8]   SOME EPIDEMIOLOGIC MODELS WITH NONLINEAR INCIDENCE [J].
HETHCOTE, HW ;
VANDENDRIESSCHE, P .
JOURNAL OF MATHEMATICAL BIOLOGY, 1991, 29 (03) :271-287
[9]   Contribution to the mathematical theory of epidemics [J].
Kermack, WO ;
McKendrick, AG .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1927, 115 (772) :700-721
[10]  
Waltman P, 1974, DETERMINISTIC THRESH