CRITICAL-BEHAVIOR OF A PROBABILISTIC-AUTOMATA NETWORK SIS MODEL FOR THE SPREAD OF AN INFECTIOUS-DISEASE IN A POPULATION OF MOVING INDIVIDUALS
CRITICAL-BEHAVIOR OF A PROBABILISTIC-AUTOMATA NETWORK SIS MODEL FOR THE SPREAD OF AN INFECTIOUS-DISEASE IN A POPULATION OF MOVING INDIVIDUALS
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DOI：
10.1088/0305-4470/26/15/020
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发表时间：
1993-08-07
期刊：
影响因子：
--
通讯作者：
CHEONG, K
中科院分区：
文献类型：
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作者：
BOCCARA, N;CHEONG, K
研究了传染病在移动个体群体中传播的概率自动机网络sis模型。本地规则由两个子规则组成。第一个，同步应用，感染和恢复模型。这是一个概率元胞自动机规则。第二个，按顺序应用，描述了个人的运动。该模型包含三个参数，感染概率p（i）和恢复概率p（r），以及每个个体尝试移动的平均次数m。根据这些参数的值，在无限的时间限制，该系统是在无病状态或在地方病状态。它从一个状态到另一个通过跨临界分岔类似于一个二阶相变的特点是一个非负序参数，其作用是发挥，在这个模型中，由受感染的个人的固定密度。本文研究了（p（i），p（r））相图和在相变点附近的侵染体稳态密度的临界行为，它们是m的函数。根据个人是否执行短期或长期的移动，它被发现，表征过渡的参数有一个质的不同的行为作为m的变化。当m非常大时，通过应用子规则建模感染和恢复所创建的相关性被破坏，并且正如预期的那样，系统的行为然后通过假设个体的均匀混合的平均场型近似正确地预测。当m不太大时，这个假设就不再正确。
A probabilistic automata network sis 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 and recovery. It is a probabilistic cellular automaton rule. The second, applied sequentially, describes the motion of the individuals. The model contains three parameters, the probabilities p(i) to get infected and p(r) to recover, and the average number of tentative moves per individual m. Depending upon the values of these parameters, in the infinite-time limit, the system is either in the disease-free state or in the endemic state. It goes from one state to the other through a transcritical bifurcation similar to a second-order phase transition characterized by a non-negative order parameter, whose role is played, in this model, by the stationary density of infected individuals. The (p(i), p(r)) phase diagram and the critical behaviour of the stationary density of infectives in the neighbourhood of the phase transition, are studied as a function of m. According to whether the individuals perform short- or long-range moves, it is found that the parameters characterizing the transition have a qualitatively different behaviour as m varies. When m is very large, the correlations created by the application of the subrule modelling infection and recovery are destroyed, and, as expected, the behaviour of the system is then correctly predicted by a mean-field-type approximation which assumes a homogeneous mixing of the individuals. When m is not large, this assumption is no longer correct.