随机种群模型中随机时间偏移分布的计算
Computation of random time-shift distributions for stochastic population models
AI总结：
本文提出一种基于函数方程求导的高效数值方法，用于计算随机种群模型的时间偏移分布，从而无需昂贵随机模拟即可生成宏观轨迹，并在流行病和病毒动力学模型上验证。
摘要：
即使在大系统中，由种群初始规模较小而产生的噪声效应也可能持续存在，并在宏观尺度上被观测到。对随机模型的确定性近似无法捕捉这一效应，但可以通过在初始条件中加入一个额外的随机时间偏移来准确近似。我们提出了一种高效的数值方法，用于计算一大类随机模型的时间偏移分布。该方法依赖于对某些函数方程的求导，我们证明当假定质量作用混合时，可以通过为常见出现的不同模型速率类型推导规则来有效地实现自动化。时间偏移分布的显式计算可用于构建一个实用工具，以高效生成随机种群模型的宏观轨迹，而无需昂贵的随机模拟。我们提供了实现该方法的完整代码，并在一个流行病模型和一个宿主体内病毒动力学模型上展示了我们的方法。
英文摘要：
Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be accurately approximated by including an additional random time-shift to the initial conditions. We present a efficient numerical method to compute this time-shift distribution for a large class of stochastic models. The method relies on differentiation of certain functional equations, which we show can be effectively automated by deriving rules for different types of model rates that arise commonly when mass-action mixing is assumed. Explicit computation of the time-shift distribution can be used to build a practical tool for the efficient generation of macroscopic trajectories of stochastic population models, without the need for costly stochastic simulations. Full code is provided to implement this and we demonstrate our method on an epidemic model and a model of within-host viral dynamics.
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