Seasonal forcing in stochastic epidemiology models

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3 Citations (Scopus)

Abstract

The goal of this paper is to motivate the need and lay the foundation for the analysis of stochastic epidemiological models with seasonal forcing. We consider stochastic SIS and SIR epidemic models, where the internal noise is due to the random interactions of individuals in the population. We provide an overview of the general theoretic framework that allows one to understand noise-induced rare events, such as spontaneous disease extinction. Although there are many paths to extinction, there is one path termed the optimal path that is probabilistically most likely to occur. By extending the theory, we have identified the quasi-stationary solutions and the optimal path to extinction when seasonality in the contact rate is included in the models. Knowledge of the optimal extinction path enables one to compute the mean time to extinction, which in turn allows one to compare the effect of various control schemes, including vaccination and treatment, on the eradication of an infectious disease.

Original languageEnglish
Pages (from-to)27-47
Number of pages21
JournalRicerche di Matematica
Volume67
Issue number1
DOIs
StatePublished - 1 Jun 2018

Fingerprint

Epidemiology
Extinction
Forcing
Stochastic models
Optimal Path
Path
SIR Epidemic Model
Epidemiological Model
Seasonality
Model
Rare Events
Vaccination
Infectious Diseases
Stationary Solutions
Stochastic Model
Likely
Contact
Internal
Interaction

Keywords

  • Epidemiology
  • Extinction
  • Rare events
  • Seasonality
  • Stochastic

Cite this

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abstract = "The goal of this paper is to motivate the need and lay the foundation for the analysis of stochastic epidemiological models with seasonal forcing. We consider stochastic SIS and SIR epidemic models, where the internal noise is due to the random interactions of individuals in the population. We provide an overview of the general theoretic framework that allows one to understand noise-induced rare events, such as spontaneous disease extinction. Although there are many paths to extinction, there is one path termed the optimal path that is probabilistically most likely to occur. By extending the theory, we have identified the quasi-stationary solutions and the optimal path to extinction when seasonality in the contact rate is included in the models. Knowledge of the optimal extinction path enables one to compute the mean time to extinction, which in turn allows one to compare the effect of various control schemes, including vaccination and treatment, on the eradication of an infectious disease.",
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Seasonal forcing in stochastic epidemiology models. / Billings, Lora; Forgoston, Eric.

In: Ricerche di Matematica, Vol. 67, No. 1, 01.06.2018, p. 27-47.

Research output: Contribution to journalArticleResearchpeer-review

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