化学反应系统中的自催化与边界稳定性
Autocatalysis and Boundary Stability in Chemical Reaction Systems
- Lawrence Technological University（劳伦斯科技大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出ALT图及其分割算法，将下一代矩阵方法从流行病学扩展到生化系统，用于计算再生数并分析边界稳定性，降低计算复杂度。
AI中文摘要：
下一代矩阵方法是计算传染病区室数学模型基本再生数的有力工具。该方法最近已被扩展到数学生物化学领域，可用于确定边界稳态的稳定与不稳定参数区域。然而，其应用中仍存在若干重大挑战，尤其是在建立该方法在生化背景下数学有效、计算可行且具有生物学意义的条件方面。在本文中，我们通过将解释从流行病学中的新感染转变为生化背景中的自催化来应对这些挑战。我们引入了一个称为ALT图（自催化-泄漏-转变图）的图，它将每个反应对雅可比矩阵的贡献分解为自催化边、泄漏边或转变边。然后，我们提出了一种系统性的ALT图分割算法，该算法保证产生有效的再生数$\ ho(FV^{-1})$，同时通过降低$FV^{-1}$的秩来降低计算复杂度。我们将该方法应用于生化反应网络和传染病传播模型。
英文摘要：
The next-generation matrix method is a powerful tool for computing the basic reproduction number in compartmental mathematical models of infectious diseases. The method has been recently extended to mathematical biochemistry, where it can be used to establish parameter regions of stability and instability for boundary steady states. Several significant challenges in its application remain, however, particularly around establishing conditions under which the method is mathematically valid, computationally tractable, and biologically meaningful in the biochemical setting. In this paper, we address these challenges by shifting the interpretation from new infections in the epidemiological setting to autocatalysis in the biochemical setting. We introduce a graph, called the ALT-graph (autocatalysis-leak-transition graph), which decomposes the contribution of each reaction to the Jacobian as autocatalytic, leak, or transition edges. We then present a systematic algorithm for splitting the ALT-graph, which is guaranteed to produce a valid reproduction number, $ρ(FV^{-1})$, while also decreasing computational complexity by lowering the rank of $FV^{-1}$. We apply the method to models of both biochemical reaction networks and infectious disease spread.
