Interplay of sources of stochastic noise in a resource-based model

Amado, André; Santana-Filho, J. V.; Campos, Paulo R. A.; Raposo, Ernesto P.

doi:10.1140/epjp/i2019-12603-5

Cited by 5 publications

(4 citation statements)

References 28 publications

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“…[ 15 , 17 , 18 ], we suppose that money cannot actually be produced (the total money balance remains constant) and, therefore, use the term “resource acquisition rate” rather than “resource production rate.” The former term was used, in particular, in Ref. [ 46 ] to describe a rate at which the agents acquire resources from the environment in a stochastic resource-based model.…”

Section: Basic Equations For An Epidemic-resource Systemmentioning

confidence: 99%

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A toy model for the epidemic-driven collapse in a system with limited economic resource

2021

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Based on a toy model for a trivial socioeconomic system, we demonstrate that the activation-type mechanism of the epidemic-resource coupling can lead to the collapsing effect opposite to thermal explosion. We exploit a SIS-like (susceptible-infected-susceptible) model coupled with the dynamics of average economic resource for a group of active economic agents. The recovery rate of infected individuals is supposed to obey the Arrhenius-like law, resulting in a mutual negative feedback between the number of active agents and resource acquisition. The economic resource is associated with the average amount of money or income per agent and formally corresponds to the effective market temperature of agents, with their income distribution obeying the Boltzmann–Gibbs statistics. A characteristic level of resource consumption is associated with activation energy. We show that the phase portrait of the system features a collapse phase, in addition to the well-known disease-free and endemic phases. The epidemic intensified by the increasing resource deficit can ultimately drive the system to a collapse at nonzero activation energy because of limited resource. We briefly discuss several collapse mitigation strategies involving either financial instruments like subsidies or social regulations like quarantine. Graphic abstract

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Section: Basic Equations For An Epidemic-resource Systemmentioning

confidence: 99%

“…The former term was used, in particular, in Ref. [46] to describe a rate at which the agents acquire resources from the environment in a stochastic resource-based model.…”

Section: Basic Equations For An Epidemic-resource Systemmentioning

confidence: 99%

A toy model for the epidemic-driven collapse in a system with limited economic resource

2021

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“…The former term was used, in particular, in Ref. [37] to describe a rate at which the agents acquire resources from the environment in a stochastic resource-based model.…”

Section: Basic Equations For An Epidemic-resource Systemmentioning

confidence: 99%

Epidemic-Driven Collapse in a System with Limited Economic Resource. II

Gandzha¹,

Kliushnichenko²,

Lukyanets³

2020

Preprint

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We consider a possibility of socioeconomic collapse caused by the spread of epidemic. To this end, we exploit a simple SIS-like (susceptible-infected-susceptible) model with negative feedback between the infected population size and a collective economic resource associated with the average amount of money or income per economic agent. The coupling mechanism in such a system is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law. In this case, economic resource formally plays the role of effective market temperature and the minimum level of resource consumption is associated with activation energy. Such a coupling can result in the collapsing effect opposite to thermal explosion, so that the epidemic could ultimately drive the system to a collapse at nonzero activation energy because of the limited resource. In this case, the system can no longer stabilize and return to the stable pre-epidemic state or a poorer post-epidemic state. We demonstrate that the system's collapse can partially be mitigated by external subsidies meaning constant resource inflow from some external source or by means of debt interpreted as a negative resource. We also consider a simple quarantine scenario and show that it can lead to different socioeconomic outcomes, depending on initial resource (market temperature) and the minimum level of resource consumption (activation energy).

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“…In particular, while Schutz et al's solu-Typeset by REVT E X tion [46] for SIR interactions on a chain with homogeneous initial conditions is a notable exception, typically analytical solutions for any fluctuation-based phenomena associated with SIR systems are absent and more complex numerical approaches are required. For the coarsergrained stochastic differential equation framework, computations typically use Euler-Maruyama [35,47], implicit Euler [38,42], or Milstein [47,48] methods, while for models capable of resolving at the level of the individual one finds numerical techniques based on Gillespie's algorithm [49,50] or direct Monte Carlo simulation [18,22] (see, also, [51]). However, these computational frameworks necessitated by the modelling at the resolution of the individual are not generally amenable to likelihood maximisation or Bayesian inference.…”

Section: Introductionmentioning

confidence: 99%

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

Souza

Araújo²,

Duarte-Filho³

et al. 2022

Phys. Rev. E

Self Cite

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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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Interplay of sources of stochastic noise in a resource-based model

Cited by 5 publications

References 28 publications

A toy model for the epidemic-driven collapse in a system with limited economic resource

A toy model for the epidemic-driven collapse in a system with limited economic resource

Epidemic-Driven Collapse in a System with Limited Economic Resource. II

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

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