Department of Mathematics, University of Arizona, Tucson, AZ, USA.
Bull Math Biol. 2022 May 28;84(7):70. doi: 10.1007/s11538-022-01026-2.
The stochastic nature of epidemic dynamics on a network makes their direct study very challenging. One avenue to reduce the complexity is a mean-field approximation (or mean-field equation) of the dynamics; however, the classic mean-field equation has been shown to perform sub-optimally in many applications. Here, we adapt a recently developed mean-field equation for SIR epidemics on a network in continuous time to the discrete time case. With this new discrete mean-field approximation, this proof-of-concept study shows that, given the density of the network, there is a strong correspondence between the epidemics on an Erdös-Rényi network and a system of discrete equations. Through this connection, we developed a parameter fitting procedure that allowed us to use synthetic daily SIR data to approximate the underlying SIR epidemic parameters on the network. This procedure has improved accuracy in the estimation of the network epidemic parameters as the network density increases, and is extremely cheap computationally.
网络上传染病动力学的随机性使得直接研究它们极具挑战性。一种降低复杂性的途径是对动力学进行平均场近似（或平均场方程）；然而，经典的平均场方程在许多应用中表现不佳。在这里，我们将最近为连续时间网络上的 SIR 传染病开发的平均场方程改编为离散时间情况。通过这个新的离散平均场近似，这个概念验证研究表明，给定网络的密度，在 Erdos-Rényi 网络上的传染病和离散方程系统之间存在很强的对应关系。通过这种联系，我们开发了一种参数拟合过程，允许我们使用合成的每日 SIR 数据来近似网络上的基本 SIR 传染病参数。随着网络密度的增加，该过程提高了对网络传染病参数估计的准确性，并且在计算上非常便宜。
