Environmental variability in a stochastic epidemic model

In this paper, we investigate the stochastic dynamics of a simple epidemic model incorporating the mean-reverting Ornstein–Uhlenbeck process analytically and numerically. We define two threshold parameters, the stochastic demographic reproduction number Rds and the stochastic basic reproduction number R0s, to utilize in identifying the stochastic extinction and persistence of the disease. We find that the stochastic disease dynamics can be determined by the environment fluctuations which measured by the intensity of volatility and the speed of reversion: the larger intensity of volatility or the smaller speed of reversion can suppress the outbreak of the disease, the smaller intensity of volatility or the the higher speed of reversion can enhance the outbreak of the disease. Furthermore, via numerical simulations, we find that the stochastic model has an endemic stationary distribution which leads to the stochastic persistence of the disease. Our results show that mean-reverting process is a well-established way of introducing stochastic environmental noise into biologically realistic population dynamic models.

• Publication year

  2018

• Venue

  Applied Mathematics and Computation

• Publication date

  2018-07-01

• Fields of study

  Mathematics, Computer Science, Environmental Science

• Identifiers
  DOI 10.1016/j.amc.2018.02.009
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• Ornstein–Uhlenbeck process is used to introduce stochastic environmental noise into the stochastic epidemic model.

  Confidence 0.91

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• Numerical simulations indicate an endemic stationary distribution, which corresponds to stochastic persistence of the disease.

  Confidence 0.90

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewq (76h6bfydm6) review--------- ✂ Cut Here ✂ --------- (jqthcshryb) review
• Larger volatility intensity or smaller speed of reversion suppresses disease outbreak, whereas smaller volatility intensity or larger speed of reversion promotes it.

  Confidence 0.94

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewq (76h6bfydm6) review--------- ✂ Cut Here ✂ --------- (jqthcshryb) review
• Stochastic demographic reproduction number Rds and stochastic basic reproduction number R0s are defined as threshold parameters for characterizing the epidemic dynamics.

  Confidence 0.96

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• endemic stationary distribution

  distribution

  A stationary probability distribution over infection states associated with sustained endemic levels.

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• ornstein–uhlenbeck process

  stochastic process

  A mean-reverting stochastic process used here to model environmental noise in the epidemic system.

  Aliases: OU process, mean-reverting process

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• speed of reversion

  parameter

  The rate at which the Ornstein–Uhlenbeck process returns toward its mean level.

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• stochastic basic reproduction number

  threshold parameter

  A threshold parameter defined for the stochastic epidemic system to characterize invasion or persistence under stochastic forcing.

  Aliases: R0s

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• stochastic demographic reproduction number

  threshold parameter

  A threshold parameter defined for the stochastic epidemic system to characterize disease dynamics under demographic stochasticity.

  Aliases: Rds

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• stochastic epidemic model

  model

  The epidemic population model analyzed under stochastic environmental forcing.

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• stochastic persistence

  dynamical behavior

  Long-term survival of the disease in the stochastic system.

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• volatility intensity

  parameter

  The magnitude parameter that controls the strength of random environmental fluctuations in the model.

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewq (76h6bfydm6) review--------- ✂ Cut Here ✂ --------- (jqthcshryb) review

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