Resilient Consensus Against Epidemic Malicious Attacks

Abstract

This paper addresses novel consensus problems for multi-agent systems operating in a pandemic environment where infectious diseases are spreading. The dynamics of the diseases follows the susceptible-infected-recovered (SIR) model, where the infection induces faulty behaviors in the agents and affects their state values. To ensure resilient consensus among the noninfectious agents, the difficulty is that the number of infectious agents changes over time. We assume that a high-level policy maker announces the level of infection in realtime, which can be adopted by the agents for their preventative measures. It is demonstrated that this problem can be formulated as resilient consensus in the presence of the socalled mobile malicious models, where the mean subsequence reduced (MSR) algorithms are known to be effective. We characterize sufficient conditions on the network structures for different policies regarding the announced infection levels and the strength of the pandemic. Numerical simulations are carried out for random graphs to verify the effectiveness of our approach. I. INTRODUCTIONRecently, the pandemic of COVID-19 has highlighted the necessity and effectiveness of unknown disease peak control. Since it may take up to several years to develop and supply vaccines sufficiently broadly [6], a large ratio of population may become infected simultaneously, which would cause huge pressure to hospitals. Initial measures such as keeping social distance and avoiding unnecessary gatherings are introduced to slow down the disease spreading. By temporarily reducing contacts with others at the proper period, peaks can be reduced in frequency and the number of infected patients. Recent works related to theoretical studies on peak control can be found in [9], [12].Epidemic models have been long studied among many different fields including mathematical biology [8], computer science [14], social science [7] and so on. Different epidemic models have been studied in the literature, but the most common ones include the susceptible-infected-susceptible (SIS) model and the susceptible-infected-recovered (SIR) model. In the traditional SIS model, the population is divided into two groups taking the susceptible and infected states; the ratios of the two groups may exhibit dynamic behaviors over time. More recently, the SIS model incorporates networks representing interactions of agents, where the pandemic process evolves over time-varying networks [15]- [17]. Similar trends can be found in the SIR model, where the agents

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