Logistic growth on networks: Exact solutions for the susceptible-infected model

Merbis, Wout; Lodato, Ivano

doi:10.1103/physreve.105.044303

Cited by 4 publications

(1 citation statement)

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“…We notice that recent studies [36,37] have applied second quantization ideas to address disease dynamics in a population. However, while in [36] a simpler model (SI, without recovered individuals) is investigated, with focus on the average sizes of the susceptible and infected subpopulations through diagrammatic expansion in small networks, in [37] the second quantization approach is specifically applied with the aim to find the set of ordinary differential equations for the average subpopulations in a SIR dynamics. In contrast, in our work these average values can be also obtained from the eigenvalues and eigenvectors of the Hamiltonian-like operator combined with the time evolution of the system's state vector.…”

Section: Introductionmentioning

confidence: 99%

Fock-space approach to stochastic susceptible-infected-recovered models

Souza

Araújo²,

Duarte-Filho³

et al. 2022

Phys. Rev. E

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We investigate the stochastic susceptible-infected-recovered (SIR) model of infectious disease dynamics in the Fock space approach. In contrast to conventional SIR models based on ordinary differential equations for the subpopulation sizes of S, I, and R individuals, the stochastic SIR model is driven by a master equation governing the transition probabilities among the system's states defined by SIR occupation numbers. In the Fock space approach the master equation is recast in the form of a real-valued Schrödinger-type equation with a second quantization Hamiltonian-like operator describing the infection and recovery processes. We find exact analytic expressions for the Hamiltonian eigenvalues for any population size N . We present small and large-N results for the average numbers of SIR individuals and basic reproduction number. For small N we also obtain the probability distributions of SIR states, epidemic sizes and durations, which cannot be found from deterministic SIR models. Our Fock space approach to stochastic SIR models introduces a powerful set of tools to calculate central quantities of epidemic processes, especially for relatively small populations where statistical fluctuations not captured by conventional deterministic SIR models play a crucial role.

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Section: Introductionmentioning

confidence: 99%