Distributed Link Removal Strategy for Networked Meta-Population Epidemics and Its Application to the Control of the COVID-19 Pandemic

This paper studies the distributed link removal problem for controlling epidemic spreading in a networked meta-population system. A deterministic networked susceptible-infected-recovered (SIR) model is considered to describe the epidemic evolving process. To curb the spread of epidemics, we reformulate the original topology design problem into a minimization program of the Perron-Frobenius eigenvalue of the matrix involving the network topology and transition rates. A modified distributed link removal strategy is developed such that it can be applied to the SIR model with heterogeneous transition rates on weighted digraphs. The proposed approach is implemented to control the COVID-19 pandemic by using the infected and recovered data reported by the German federal states. The numerical experiment shows that the infected percentage can be significantly reduced by employing the distributed link removal strategy.

I. Introduction

Various models have been proposed to mathematically characterize the spread of epidemics [1]–[3]. Among them, the compartmental models, e.g., the susceptible-infected-susceptible (SIS) model and the susceptible-infected-recovered (SIR) model, play the fundamental role. One important class of the compartmental models is the scalar deterministic models, which can be referred to in the survey [4]. These models have been widely investigated and qualitatively characterize the macroscopic behavior of the dynamics of infectious diseases, for example, the COVID19 pandemic [3]. However, the drawback of the scalar models is that they are based on the hidden assumption that there exists a well-mixed population, i.e., individuals have the same chances to interact with each other. In fact, this assumption introduces not only the homogeneity in network structure but also in individual behaviors, which does not generally hold in the globalized world with close connection via, for instance, face-to-face social networks and traffic networks. Both of these heterogeneities, nonetheless, play significant roles in shaping the epidemic spreading process. This brings us to the network epidemic models, where the nodal dynamics are considered [2]. There are two kinds of interpretations of the network epidemic models: (a) the disease spreads on a network where each node represents one individual and (b) the disease spreads on a network of interconnected sub-population (groups of populations), i.e., meta-population. Clearly, the meta-population interpretation provides an efficient and comprehensive way of depicting pandemics that break out world-wide and spread rapidly in communities. Thus, in this paper, we investigate the control strategy for networked meta-population epidemics.