scholarly journals Underdetection in a stochastic SIR model for the analysis of the COVID-19 Italian epidemic

2021 ◽  
Author(s):  
Antonella Bodini ◽  
Sara Pasquali ◽  
Antonio Pievatolo ◽  
Fabrizio Ruggeri
Keyword(s):  
Sir Model ◽  
Stochastic Sir ◽  
Stochastic Sir Model

scholarly journals Modelling the spread of American foulbrood in honeybees

2013 ◽  
Vol 10 (88) ◽  
pp. 20130650 ◽  
Author(s):  
Samik Datta ◽  
James C. Bull ◽  
Giles E. Budge ◽  
Matt J. Keeling
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Control Strategies ◽  
Sir Model ◽  
Model Parameters ◽  
American Foulbrood ◽  
Inspection Period ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae , that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.

scholarly journals Stochastic SIR model with jumps

2013 ◽  
Vol 26 (8) ◽  
pp. 867-874 ◽  
Author(s):  
Xianghua Zhang ◽  
Ke Wang
Keyword(s):  
Sir Model ◽  
Stochastic Sir ◽  
Stochastic Sir Model

scholarly journals The use of mixture-density networks in the emulation of complex epidemiological individual-based models

2019 ◽  
Author(s):  
Christopher N Davis ◽  
T Deirdre Hollingsworth ◽  
Quentin Caudron ◽  
Michael A Irvine
Keyword(s):  
Neural Network ◽  
Infectious Disease ◽  
Negative Binomial ◽  
Sir Model ◽  
Discrete Distributions ◽  
Individual Based Model ◽  
Mixture Density ◽  
Individual Based Models ◽  
Stochastic Sir ◽  
Stochastic Sir Model

AbstractComplex, highly computational, individual-based models are abundant in epidemiology. For epidemics such as macro-parasitic diseases, detailed modelling of human behaviour and pathogen life-cycle are required in order to produce accurate results. This can often lead to models that are computationally-expensive to analyse and perform model fitting, and often require many simulation runs in order to build up sufficient statistics. Emulation can provide a more computationally-efficient output of the individual-based model, by approximating it using a statistical model. Previous work has used Gaussian processes in order to achieve this, but these can not deal with multi-modal, heavy-tailed, or discrete distributions. Here, we introduce the concept of a mixture density network (MDN) in its application in the emulation of epidemiological models. MDNs incorporate both a mixture model and a neural network to provide a flexible tool for emulating a variety of models and outputs. We develop an MDN emulation methodology and demonstrate its use on a number of simple models incorporating both normal, gamma and beta distribution outputs. We then explore its use on the stochastic SIR model to predict the final size distribution and infection dynamics. MDNs have the potential to faithfully reproduce multiple outputs of an individual-based model and allow for rapid analysis from a range of users. As such, an open-access library of the method has been released alongside this manuscript.Author summaryInfectious disease modellers have a growing need to expose their models to a variety of stakeholders in interactive, engaging ways that allow them to explore different scenarios. This approach can come with a considerable computational cost that motivates providing a simpler representation of the complex model. We propose the use of mixture density networks as a solution to this problem. These are highly flexible, deep neural network-based models that can emulate a variety of data, including counts and over-dispersion. We explore their use firstly through emulating a negative-binomial distribution, which arises in many places in ecology and parasite epidemiology. We then explore the approach using a stochastic SIR model. We also provide an accompanying Python library with code for all examples given in the manuscript. We believe that the use of emulation will provide a method to package an infectious disease model such that it can be disseminated to the widest audience possible.

scholarly journals Asymptotic behavior of global positive solution to a stochastic SIR model

2011 ◽  
Vol 54 (1-2) ◽  
pp. 221-232 ◽  
Author(s):  
Daqing Jiang ◽  
Jiajia Yu ◽  
Chunyan Ji ◽  
Ningzhong Shi
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solution ◽  
Sir Model ◽  
Global Positive Solution ◽  
Stochastic Sir ◽  
Stochastic Sir Model
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