Network Lyapunov Functions for Epidemic Models
Network Lyapunov Functions for Epidemic Models
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DOI：
10.1109/cdc42340.2020.9304021
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
M. Newton;A. Papachristodoulou
中科院分区：
文献类型：
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作者：
M. Newton;A. Papachristodoulou
更好地了解一种流行病的行为的愿望从未像现在这样重要。流行病模型不仅为预测疾病的传播提供了重要工具，而且在模拟在线网络上的谣言传播和计算机病毒在互联网上的分布方面也有其他用途。在本文中，我们使用的易感-暴露-隐藏-隐藏（SEIR）模型，沿着一个扩展的多种群模型，可以显示更丰富的动态。以前，一个对角李雅普诺夫函数的对数线性结构已被证明存在一些假设下，为单一和多人口的情况下。然而，当再生数小于1或子系统之间的网络不是强连通的，没有多种群李雅普诺夫函数是已知的。我们提出了一种替代的李雅普诺夫函数结构的两个人口模型，已被证明是有效的，在许多情况下与平方和规划。这些实例包括原来的对数线性李雅普诺夫函数失败的条件，这意味着我们已经构建了一个李雅普诺夫函数的SEIR多人口模型的第一次。然后，可以使用先进的技术将这种方法扩展到一般的多种群情况。
The desire to better understand the behaviour of an epidemic has never been more important. Not only do epidemic models provide vital tools for predicting the spread of a disease, but they have also seen other uses in modelling the propagation of rumour spreading on online networks and the distribution of computer viruses over the internet. In this paper we use the Susceptible-Exposed-Infected-Recovered (SEIR) model, along with an extended multi-population model that can display richer dynamics. Previously, a diagonal Lyapunov function of a log-linear structure has been shown to exist under some assumptions, for both the single and multi-population cases. However, when the reproduction number is less than unity or the network between subsystems is not strongly connected, no multi-population Lyapunov function is known. We propose an alternative Lyapunov function structure for a two-population model, that has been shown to be valid for many instances with Sum of Squares programming. These instances include conditions where the original log-linear Lyapunov function fails, meaning that we have constructed a Lyapunov function for an SEIR multi-population model for the first time. This approach can then be scaled up to the general multi-population case using advanced techniques.