Accurate noise projection for reduced stochastic epidemic models

Forgoston, Eric; Billings, Lora; Schwartz, Ira B.

doi:10.1063/1.3247350

Cited by 28 publications

(39 citation statements)

References 38 publications

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“…For example, in a Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model, there are terms at low order in the normal form transform which cause a significant difference between the average stochastic center manifold and the deterministic manifold [21]. Therefore, when working with the SEIR model, one must use the stochastic normal form coordinate transform approach to obtain the correct projection of the noise onto the center manifold.…”

Section: Discussionmentioning

confidence: 99%

Escape Rates in a Stochastic Environment with Multiple Scales

Forgoston¹,

Schwartz²

2009

SIAM J. Appl. Dyn. Syst.

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Abstract. We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic center manifold followed by a "naïve" replacement of the stochastic term. The second method allows one to more accurately describe the stochastic effects and involves the derivation of a normal form coordinate transform that is used to find the stochastic center manifold. The results of both methods are used along with the path integral formalism of large fluctuation theory to predict the escape rate from one basin of attraction to another. The general theory is applied to the example of a surface flow described by a generic, singularly perturbed, damped, nonlinear oscillator with additive, Gaussian noise. We show how both nonlinear reduction methods compare in escape rate scaling. Additionally, the center manifolds are shown to predict high pre-history probability regions of escape. The theoretical results are confirmed using numerical computation of the mean escape time and escape prehistory, and we briefly discuss the extension of the theory to stochastic control.

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Section: Discussionmentioning

confidence: 99%

Escape Rates in a Stochastic Environment with Multiple Scales

Forgoston¹,

Schwartz²

2009

SIAM J. Appl. Dyn. Syst.

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“…And there is still an ongoing debate on generalizations to stochastic dynamical processes (see e.g. [10]). …”

Section: Introductionmentioning

confidence: 99%

Time-scale separation and centre manifold analysis describing vector-borne disease dynamics

Rocha

Aguiar

Souza

et al. 2013

International Journal of Computer Mathematics

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In vector-borne diseases, the human hosts' epidemiology often acts on a much slower time scales than the one of the mosquitos transmitting as a vector from human to human, due to their vastly different life cycles. We investigate in how far the fast time scale of the mosquito epidemiology can be slaved by the slower human epidemiology, so that for the understanding of human disease data mainly the dynamics of the human time scale is essential and only slightly perturbed by the mosquito dynamics.

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“…In a previous paper (Forgoston et al 2009), we showed how noise affects the timing of outbreaks for a time independent system. Therefore, it was concluded that it is essential to produce a low-dimensional system which captures the correct timing of the outbreaks as well as the amplitude and phase of any recurrent behavior for any given measured realization of an outbreak.…”

Section: Introductionmentioning

confidence: 98%

Predicting Unobserved Exposures from Seasonal Epidemic Data

Forgoston

Schwartz

2013

Bull Math Biol

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We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a data-based model prediction of the number of unobserved exposed individuals over very long times.

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Accurate noise projection for reduced stochastic epidemic models

Cited by 28 publications

References 38 publications

Escape Rates in a Stochastic Environment with Multiple Scales

Escape Rates in a Stochastic Environment with Multiple Scales

Time-scale separation and centre manifold analysis describing vector-borne disease dynamics

Predicting Unobserved Exposures from Seasonal Epidemic Data

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