Multi-compartment linear noise approximation

Challenger, Joseph D.; McKane, Alan J.; Pahle, Jürgen

doi:10.1088/1742-5468/2012/11/p11010

Cited by 8 publications

(8 citation statements)

References 28 publications

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“…More compartments than one are also found in Challenger et al. (2012). The equations of LNA with spatial variation are derived in Scott et al.…”

Section: Introductionsupporting

confidence: 64%

The Linear Noise Approximation for Spatially Dependent Biochemical Networks

Lötstedt

2018

Bull Math Biol

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An algorithm for computing the linear noise approximation (LNA) of the reaction-diffusion master equation (RDME) is developed and tested. The RDME is often used as a model for biochemical reaction networks. The LNA is derived for a general discretization of the spatial domain of the problem. If M is the number of chemical species in the network and N is the number of nodes in the discretization in space, then the computational work to determine approximations of the mean and the covariances of the probability distributions is proportional to M 2 N 2 in a straightforward implementation. In our LNA algorithm, the work is proportional to M 2 N . Since N usually is larger than M, this is a significant reduction. The accuracy of the approximation in the algorithm is estimated analytically and evaluated in numerical experiments.

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“…More compartments than one are also found in Challenger et al. (2012). The equations of LNA with spatial variation are derived in Scott et al.…”

Section: Introductionsupporting

confidence: 64%

The Linear Noise Approximation for Spatially Dependent Biochemical Networks

Lötstedt

2018

Bull Math Biol

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“…(30) (sometimes referred to as the multi-compartment LNA [24]). Additionally this spatiallyextended reaction system satisfies the four constraints mentioned in Section III.A and hence it follows by the results of Section III that the multi-compartment LNA and the RDME agree to second-order moments in the molecule number fluctuations in each of the boxes composing space.…”

Section: A Spatially Extended Systemsmentioning

confidence: 99%

Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems

Grima

2015

Phys. Rev. E

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“…The LNA has been successfully applied to describe intrinsic stochastic fluctuations in various contexts [44][45][46] and has a solid theoretical basis [47,48]. The LNA provides accurate approximation for large populations or when the fluctuations are small compared to the steady state of the system.…”

Section: Discussionmentioning

confidence: 99%

A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models

Zimmer

Yaesoubi²,

Cohen

2017

PLoS Comput Biol

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Stochastic transmission dynamic models are especially useful for studying the early emergence of novel pathogens given the importance of chance events when the number of infectious individuals is small. However, methods for parameter estimation and prediction for these types of stochastic models remain limited. In this manuscript, we describe a calibration and prediction framework for stochastic compartmental transmission models of epidemics. The proposed method, Multiple Shooting for Stochastic systems (MSS), applies a linear noise approximation to describe the size of the fluctuations, and uses each new surveillance observation to update the belief about the true epidemic state. Using simulated outbreaks of a novel viral pathogen, we evaluate the accuracy of MSS for real-time parameter estimation and prediction during epidemics. We assume that weekly counts for the number of new diagnosed cases are available and serve as an imperfect proxy of incidence. We show that MSS produces accurate estimates of key epidemic parameters (i.e. mean duration of infectiousness, R0, and Reff) and can provide an accurate estimate of the unobserved number of infectious individuals during the course of an epidemic. MSS also allows for accurate prediction of the number and timing of future hospitalizations and the overall attack rate. We compare the performance of MSS to three state-of-the-art benchmark methods: 1) a likelihood approximation with an assumption of independent Poisson observations; 2) a particle filtering method; and 3) an ensemble Kalman filter method. We find that MSS significantly outperforms each of these three benchmark methods in the majority of epidemic scenarios tested. In summary, MSS is a promising method that may improve on current approaches for calibration and prediction using stochastic models of epidemics.

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Multi-compartment linear noise approximation

Cited by 8 publications

References 28 publications

The Linear Noise Approximation for Spatially Dependent Biochemical Networks

The Linear Noise Approximation for Spatially Dependent Biochemical Networks

Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems

A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models

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