Markovian SIR model for opinion propagation

E. D. Cuypere, K. D. Turck, S. Wittevrongel, D. Fiems
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引用次数: 8

Abstract

In this work, we propose a new model for the dynamics of single opinion propagation at a size-limited location with a low population turnover. This means that a maximum number of individuals can be supported by the location and that the allowed individuals have a long sojourn time before leaving the location. The individuals can have either no opinion (S), a strong opinion that they want to spread (I), or an opinion that they keep for themselves (R); the letters stem from the popular Susceptible-Infectious-Recovered (SIR) epidemic model. Furthermore, we consider a variable opinion transmission rate. Hence, the opinion spreading is modelled as a Markovian non-standard SIR epidemic model with stochastic arrivals, departures, infections and recoveries. We evaluate the system performance by two complementary approaches: we apply a numerical but approximate solution approach which relies on Maclaurin series expansions and we investigate the fluid limit of the system at hand. Finally, we illustrate our approach by some numerical examples.
意见传播的马尔可夫SIR模型
在这项工作中,我们提出了一个新的模型,用于在人口流动率低的规模有限的地点进行单一意见传播的动态。这意味着该地点可以支持最大数量的个人,并且允许的个人在离开该地点之前有很长的逗留时间。个人可以没有意见(S),有强烈的意见想要传播(I),或者有自己的意见(R);这些字母来自流行的易感-感染-恢复(SIR)流行病模型。此外,我们考虑一个可变的意见传输率。因此,将观点传播建模为具有随机到达、离开、感染和恢复的马尔可夫非标准SIR流行病模型。我们用两种互补的方法来评估系统的性能:我们采用一种依赖于麦克劳林级数展开的数值近似解方法,我们研究了系统的流体极限。最后,我们用一些数值例子来说明我们的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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