An Introduction to Compartmental Modeling for the Budding Infectious Disease Modeler

Blackwood, Julie C.; Childs, Lauren M.

doi:10.30707/lib5.1blackwood

Cited by 130 publications

(99 citation statements)

References 15 publications

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“…Mathematical models of disease spread assume that a population within a compartment (e.g., city, region, country) can be subdivided into a set of distinct classes [11]. The SIR model classifies individuals in the compartment as one of three classes: susceptible (S), infectious (I), and recovered or removed (R).…”

Section: Definitions and Nomenclaturementioning

confidence: 99%

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Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics

et al. 2020

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The SIR ('susceptible-infectious-recovered') formulation is used to uncover the generic spread mechanisms observed by COVID-19 dynamics globally, especially in the early phases of infectious spread. During this early period, potential controls were not effectively put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of COVID-19 basic reproduction number R o inferred from SIR formulation. The work here shows that there is global convergence (i.e., across many nations) to an uncontrolled R o = 4.5 that describes the early time spread of COVID-19. This value is in agreement with independent estimates from other sources reviewed here and adds to the growing consensus that the early estimate of R o = 2.2 adopted by the World Health Organization is low. A reconciliation between power-law and exponential growth predictions is also featured within the confines of the SIR formulation. The effects of testing ramp-up and the role of 'super-spreaders' on the inference of R o are analyzed using idealized scenarios. Implications for evaluating potential control strategies from this uncontrolled R o are briefly discussed in the context of the maximum possible infected fraction of the population (needed to assess health care capacity) and mortality (especially in the USA given diverging projections). Model results indicate that if intervention measures still result in R o > 2.7 within 44 days after first infection, intervention is unlikely to be effective in general for COVID-19.

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Section: Definitions and Nomenclaturementioning

confidence: 99%

“…The classic susceptible-infectious-recovered (SIR) paradigm, initiated in the late 1920s [6], now provides a mathematical framework that describes the core transmission dynamics of a wide range of human diseases [7][8][9][10][11][12], including COVID-19 [13]. A key parameter in the SIR paradigm is the basic reproduction number (R o ).…”

Section: Introductionmentioning

confidence: 99%

Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics

et al. 2020

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“…Compartmental models are a class of models that is widely used in epidemiology to model transitions between various stages of disease [1,8,9]. We now introduce the Susceptible-Exposed-Infectious-Recovered (SEIR) and the related Susceptible-Infectious-Recovered (SIR) compartmental models that have been dominant in COVID-19 modelling literature [1,5,6,10].…”

Section: Epidemiological Modellingmentioning

confidence: 99%

Bayesian inference of COVID-19 spreading rates in South Africa

Mbuvha

Marwala

2020

PLoS ONE

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The Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has highlighted the need for performing accurate inference with limited data. Fundamental to the design of rapid state responses is the ability to perform epidemiological model parameter inference for localised trajectory predictions. In this work, we perform Bayesian parameter inference using Markov Chain Monte Carlo (MCMC) methods on the Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological models with time-varying spreading rates for South Africa. The results find two change points in the spreading rate of COVID-19 in South Africa as inferred from the confirmed cases. The first change point coincides with state enactment of a travel ban and the resultant containment of imported infections. The second change point coincides with the start of a state-led mass screening and testing programme which has highlighted community-level disease spread that was not well represented in the initial largely traveller based and private laboratory dominated testing data. The results further suggest that due to the likely effect of the national lockdown, community level transmissions are slower than the original imported case driven spread of the disease.

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“…This parameter is equivalent to the basic reproductive ratio (R 0 ) which is defined as the expected number of secondary infections in a population of Susceptible receptors arising from a single individual during their entire infectious period and it often serves as a threshold parameter that predicts whether an infection will spread. The basic reproductive ratio (R 0 ) is the product of the transmission rate and the average amount of time a receptor spends in the Infectious state and, the larger its value, the harder it will be to eradicate the microparasite or non-native species (Blackwood and Childs 2018). For non-native species, the duration of the Infectious state can be many decades so even if transmission rates are low, R 0 will be much greater than 1.0 and the invasion will persist.…”

Section: Towards a Basic Reproductive Ratio R 0 For Biological Invasionsmentioning

confidence: 99%

“…1A) in which receptors (e.g. hosts) are categorised into three compartments: Susceptible, Infectious and Resistant (sometimes classed as Removed or Recovered), based on their infection status (Blackwood and Childs 2018;Gilligan 2008;Kleczkowski et al 2019). Some infections do not provide long-lasting acquired immunity (e.g.…”

Section: Introductionmentioning

confidence: 99%

The Epidemiological Framework for Biological Invasions (EFBI): an interdisciplinary foundation for the assessment of biosecurity threats

Hulme¹,

Baker²,

Freckleton³

et al. 2020

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Emerging microparasite (e.g. viruses, bacteria, protozoa and fungi) epidemics and the introduction of non-native pests and weeds are major biosecurity threats worldwide. The likelihood of these threats is often estimated from probabilities of their entry, establishment, spread and ease of prevention. If ecosystems are considered equivalent to hosts, then compartment disease models should provide a useful framework for understanding the processes that underpin non-native species invasions. To enable greater cross-fertilisation between these two disciplines, the Epidemiological Framework for Biological Invasions (EFBI) is developed that classifies ecosystems in relation to their invasion status: Susceptible, Exposed, Infectious and Resistant. These states are linked by transitions relating to transmission, latency and recovery. This viewpoint differs markedly from the species-centric approaches often applied to non-native species. It allows generalisations from epidemiology, such as the force of infection, the basic reproductive ratio R0, super-spreaders, herd immunity, cordon sanitaire and ring vaccination, to be discussed in the novel context of non-native species and helps identify important gaps in the study of biological invasions. The EFBI approach highlights several limitations inherent in current approaches to the study of biological invasions including: (i) the variance in non-native abundance across ecosystems is rarely reported; (ii) field data rarely (if ever) distinguish source from sink ecosystems; (iii) estimates of the susceptibility of ecosystems to invasion seldom account for differences in exposure to non-native species; and (iv) assessments of ecosystem susceptibility often confuse the processes that underpin patterns of spread within -and between- ecosystems. Using the invasion of lakes as a model, the EFBI approach is shown to present a new biosecurity perspective that takes account of ecosystem status and complements demographic models to deliver clearer insights into the dynamics of biological invasions at the landscape scale. It will help to identify whether management of the susceptibility of ecosystems, of the number of vectors, or of the diversity of pathways (for movement between ecosystems) is the best way of limiting or reversing the population growth of a non-native species. The framework can be adapted to incorporate increasing levels of complexity and realism and to provide insights into how to monitor, map and manage biological invasions more effectively.

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An Introduction to Compartmental Modeling for the Budding Infectious Disease Modeler

Cited by 130 publications

References 15 publications

Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics

Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics

Bayesian inference of COVID-19 spreading rates in South Africa

The Epidemiological Framework for Biological Invasions (EFBI): an interdisciplinary foundation for the assessment of biosecurity threats

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