AI 中文总结
本文提出无自由参数的耦合一阶微分方程动力学模型，通过数学分析复现多种抑郁相关病程，配套网页工具支持交互式实验。
AI 中文摘要
本文提出了一个用于（临床）抑郁症的基础动力学模型，以描述两个耦合状态的时间演化：心理韧性水平与抑郁症状。心理韧性水平也可通过对过往症状的记忆来解释。该模型由两个耦合的一阶微分方程组成，无自由参数，无需从神经科学第一性原理推导的额外开销，即可定性捕捉不同的病程。本文对该模型进行了全面的数学分析，包括平衡点、稳定性特性与单调性。该模型可复现文献中常见的慢性、延迟、康复及韧性场景，还能复现诸如既有症状改善、低强度逆境导致的倦怠，或孤立复发性抑郁发作等场景。文稿配套了计算工具，可复现图表，且无需预先具备数学或编程技能即可在网页浏览器中交互式实验该模型（网址为this https URL）。
英文摘要
A basic dynamical model for (clinical) depression is presented to describe the time evolution of two coupled states: a resilience level and a depression symptom. The resilience level can also be interpreted in terms of the memory of past symptoms. The model consists of a system of two coupled first order differential equations without free parameters that qualitatively captures different courses of illness, without the overhead of a derivation from neuroscientific first principles. A comprehensive mathematical analysis of the model is provided, including equilibria, stability properties, and monotonicity. The model can reproduce chronic, delayed, recovery, and resilience scenarios that are prominent in the literature, as well as scenarios such as improvement from pre-existing conditions, burnout from low-grade adversity, or isolated and recurrent depressive episodes. Supplementary to the manuscript are computational tools to replicate the figures and, without prior mathematical or programming skills, to experiment with the model interactively in the web browser (at https://rsmodel.org/).
Comments29 pages, 22 figures
