Non-universal power-law dynamics of SIR models on hierarchical modular networks

Abstract

Power-law (PL) time dependent infection growth has been reported in many COVID-19 statistics. In simple SIR models the number of infections grows at the outbreak as $I(t)\propto t^{d-1}$ on $d$-dimensional Euclidean lattices in the endemic phase or follow a slower universal PL at the critical point, until finite sizes cause immunity and a crossover to an exponential decay. Heterogeneity may alter the dynamics of spreading models, spatially inhomogeneous infection rates can cause slower decays, posing a threat of a long recovery from a pandemic. COVID-19 statistics have also provided epidemic size distributions with PL tails in several countries. Here I investigate SIR like models on hierarchical modular networks, embedded in 2d lattices with the addition of long-range links. I show that if the topological dimension of the network is finite, average degree dependent PL growth of prevalence emerges. Supercritically the same exponents as of regular graphs occurs, but the topological disorder alters the critical behavior. This is also true for the epidemic size distributions. Mobility of individuals does not affect the form of the scaling behavior, except for the $d=2$ lattice, but increases the magnitude of the epidemic. The addition of a super-spreader hot-spot also does not change the growth exponent and the exponential decay in the herd immunity regime.

arXiv comment9 pages, 13 figures, slightly updated, accepted version to appear in PRE

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• Epidemic processes in complex networks
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Average path length in random networks
• Average path length in uncorrelated random networks with hidden variables
• Avalanche and spreading exponents in systems with absorbing states
• Power-law distribution in the number of confirmed COVID-19 cases
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• Griffiths phases and localization in hierarchical modular networks
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• Transitions in spatial networks

Cited by in corpus (2)

• Critical behavior of the diffusive susceptible-infected-recovered model
• Effects of lattice dilution on the non-equilibrium phase transition in the stochastic Susceptible-Infectious-Recovered model