网络上基于个体的流行病动力学的无方程多尺度计算分析
Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks
AI总结：
提出无方程方法与模拟退火优化相结合，从基于个体的微观模拟中提取粗粒度系统级分析，高效计算稳态、分岔及稳定性，避免显式宏观闭包。
摘要：
流行病动力学的监测、分析以及最终高效长期预测和控制是当今主要挑战之一。详细的原子论数学模型对此目标起着重要作用。本文展示了如何利用无方程方法和模拟退火等优化技术，将基于个体的详细流行病模拟与粗粒度、系统级分析联系起来。该方法提供了一种系统性的途径，用于分析复杂/多尺度流行病模拟器的参数行为，其效率远高于简单的时间正向模拟。本文展示了如何以直接的方式执行稳态和（如果需要）时间相关计算、稳定性计算以及延拓和数值分岔分析。该方法通过一个部署在随机正则连通图上的简单基于个体的流行病模型进行说明。使用基于个体的微观模拟器作为黑箱粗粒度时间步进器，并借助模拟退火，计算了粗粒度平衡分岔图，并分析了稳态的稳定性，从而避免了在成对表示视角下获得宏观水平显式闭包的必要性。
英文摘要：
The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be one of the major challenges nowadays. Detailed atomistic mathematical models play an important role towards this aim. In this work it is shown how one can exploit the Equation Free approach and optimization methods such as Simulated Annealing to bridge detailed individual-based epidemic simulation with coarse-grained, systems-level, analysis. The methodology provides a systematic approach for analyzing the parametric behavior of complex/ multi-scale epidemic simulators much more efficiently than simply simulating forward in time. It is shown how steady state and (if required) time-dependent computations, stability computations, as well as continuation and numerical bifurcation analysis can be performed in a straightforward manner. The approach is illustrated through a simple individual-based epidemic model deploying on a random regular connected graph. Using the individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing I compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level under a pairwise representation perspective.
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