Estimating Contagion Dynamical Model on Networks via Data Assimilation

Yinchong WangWenlian Lu^*

• Fudan University, Shanghai, China

In this paper, we proposed a data assimilation method for estimating the states, parameters, and hyperparameters of the network-based contagion dynamics models with heterogeneous parameters via ensemble Kalman filter approaches, based on the macroscopic data, that is, not the information of each individual node, but rather some statistical information, such as the average infection rate and average recovery rate of an epidemic. The proposed methods were validated using a network-based susceptible-infectious-recovery dynamical model in several scenarios: (i) homogeneous parameters (all nodes share the same infection and recovery rate parameters) with known network topological structures (the connections between each node are assumed to be known); (ii) heterogeneous parameters with known network topological structures (the parameters of each node are assumed to be sampled from certain distributions with unknown hyperparameters); and (iii) homogeneous parameters with unknown network topological structures (the distribution of this network topological structure is assumed to be known). Numerical examples demonstrate that the proposed algorithms are efficient in estimating the states, parameters, and hyperparameters with good performance when the network size is sufficiently large. This indicates that the proposed method is promising for estimating the network-based contagion dynamics model from macro observations without monitoring node-level states [22,25].