论文标题
使用广义线性链技巧和连续时间马尔可夫链理论建造平均场状态过渡模型
Building Mean Field State Transition Models Using The Generalized Linear Chain Trick and Continuous Time Markov Chain Theory
论文作者
论文摘要
众所周知的线性链技巧（LCT）允许建模者通过依次通过子群链依次过渡个体，从而得出假设伽马（Erlang）分布式通道时间的平均场频率。在这些状态下花费的时间是$ k $成倍分布的随机变量的总和，因此是伽玛（erlang）分布式的。广义的线性链技巧（GLCT）将此技术扩展到更广泛的相型分布族，其中包括指数，Erlang，低指数和Coxian分布。凭直觉，相型分布是连续时间马尔可夫链（CTMC）的吸收时间分布。在这里，我们回顾了CTMC和相类型分布，然后说明如何使用GLCT从基本的随机模型假设中有效地构建平均场ODE模型。我们概括了Rosenzweig-Macarthur和Seir模型，并显示了使用GLCT计算数值解决方案的好处。这些结果突出了使用GLCT从第一原理中得出ODE模型的一些实际好处和直观的性质。
The well-known Linear Chain Trick (LCT) allows modelers to derive mean field ODEs that assume gamma (Erlang) distributed passage times, by transitioning individuals sequentially through a chain of sub-states. The time spent in these states is the sum of $k$ exponentially distributed random variables, and is thus gamma (Erlang) distributed. The Generalized Linear Chain Trick (GLCT) extends this technique to the much broader phase-type family of distributions, which includes exponential, Erlang, hypoexponential, and Coxian distributions. Intuitively, phase-type distributions are the absorption time distributions for continuous time Markov chains (CTMCs). Here we review CTMCs and phase-type distributions, then illustrate how to use the GLCT to efficiently build mean field ODE models from underlying stochastic model assumptions. We generalize the Rosenzweig-MacArthur and SEIR models and show the benefits of using the GLCT to compute numerical solutions. These results highlight some practical benefits, and the intuitive nature, of using the GLCT to derive ODE models from first principles.
