Immunization strategies for simplicial irreversible epidemic on simplicial complex

Higher-order networks can be used to describe the interaction of multiple entities in real-world collective behaviors such as dining, conference attendance, and public transportation use. Collective behavior is often one of the main reasons for “super-spreading events” during epidemics. How to propose effective immunization strategies is a Frontier research topic in network science and public health. To the best of our knowledge, there is a lack of systematic research on immunization strategies for epidemics on higher-order networks. We use synthetic networks and real-world networks as underlying structures to construct simplicial complexes to describe higher-order interaction networks, including pairwise and group interactions, and then propose a simplicial irreversible epidemic spreading model (i.e., simplicial Susceptible-Infected-Removed model). The temporal evolution process of nodes in different states in the system is described by extending the Microscopic Markov Chain Approach. Based on the node degree index and betweenness index, immunization strategies are proposed on the higher-order networks. Through theoretical analysis and numerical simulations, we discuss the effects of different higher-order infection rates, immunization ratios, and immunization strategies on the simplicial irreversible epidemic spread. Under some specific parameter configurations, we observe continuous growth, discontinuous growth, reduction of outbreak threshold, etc.