Title: Computation of random time-shift distributions for stochastic population models Show Chinese title

Title: 随机时间位移分布的计算对于随机种群模型

Abstract: 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. Show Chinese abstract

Abstract: 即使在大型系统中，当种群最初较小时产生的噪声效应也可能在宏观尺度上保持可测量。 对随机模型的确定性近似无法捕捉这种效应，但可以通过在初始条件中包含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。 该方法依赖于某些泛函方程的微分，我们通过推导在假设质量作用混合时常见的模型速率类型的不同规则，证明这些可以有效地自动化。 显式计算时间偏移分布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，而无需进行昂贵的随机模拟。 提供了完整的代码来实现这一点，并我们在流行病模型和宿主内病毒动力学模型上展示了我们的方法。