Modern view of network resilience and epidemic spreading has been shaped by percolation tools from statistical physics, where nodes and edges are removed or immunized randomly from a large-scale network. In this paper, we produce a theoretical framework for studying targeted immunization in networks, where only nodes can be observed at a time with the most connected one among them being immunized and the immunity it has acquired may be lost subject to a decay probability . We examine analytically the percolation properties as well as scaling laws, which uncover distinctive characters for Erdős–Rényi and power-law networks in the two dimensions of and . We study both the case of a fixed immunity loss rate as well as an asymptotic total loss scenario, paving the way to further understand temporary immunity in complex percolation processes with limited knowledge.
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2021
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