What the reproductive number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e629" altimg="si18.svg"><mml:msub><mml:mrow><mml:mi mathvariant="script" class="EuScript">R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> can and cannot tell us about COVID-19 dynamics

Shaw, Cheng-Kuang; Kennedy, David

doi:10.1016/j.tpb.2020.12.003

Cited by 34 publications

(25 citation statements)

References 112 publications

(142 reference statements)

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“…See Figure 4 Example 6. The SI aps QR model (with asymptomatic, pre-symptomatic, and symptomatic infectious) [37,56] (3.2). See Figure 5; The disease states are i = ( i a , i p , i s , q), and the model is defined by…”

Section: Examples Of Sir-ph Models Used In Covid-19 Modellingmentioning

confidence: 99%

“…We begin by recalling in Section 2 several basic explicit formulas for the SIR model. Section 3 presents the corresponding SIR-PH generalizations, and Section 4 offers some applications: the SEIHRD model [23][24][25][26][27], which adds to the classic SEIR (susceptible + exposed + infectious + recovered) a hospitalized (H) class and a dead class (D); the SEICHRD model [28] which adds a critically ill class (C); the SEIARD [29] and SEIAHR/SEIRAH(D) models [30][31][32][33][34][35][36], which add an asymptomatic class (A); and the SI 3 QR model [37]. This is just a sample chosen from some of our favorite COVID papers.…”

Section: Introductionmentioning

confidence: 99%

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A Review of Matrix SIR Arino Epidemic Models

2021

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Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number R has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for (x,y,z) models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity Y(t) which satisfies “classic SIR relations”, which may be useful to obtain approximate control policies.

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Section: Examples Of Sir-ph Models Used In Covid-19 Modellingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Review of Matrix SIR Arino Epidemic Models

2021

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“…Implicitly, however, estimates of such dynamic parameters like β or γ may fluctuate because of societal responses, temporary biases in reporting, etc. Regime regression can truncate epidemic data, thereby eliminating dynamic complications that can muddy the interpretation of estimates of initial parameters like R 0 [11].…”

Section: Plos Onementioning

confidence: 99%

“…The beginning of an epidemic therefore displays a simplicity lacking during the middle of the epidemic and its dynamic complexities [11]. In fact, the initial exponential phase develops from a fixed interaction between an infectious agent and a population in steady state.…”

Section: Introductionmentioning

confidence: 99%

A comprehensive estimation of country-level basic reproduction numbers R0 for COVID-19: Regime regression can automatically estimate the end of the exponential phase in epidemic data

Spouge

2021

PLoS ONE

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In a compartmental epidemic model, the initial exponential phase reflects a fixed interaction between an infectious agent and a susceptible population in steady state, so it determines the basic reproduction number R0 on its own. After the exponential phase, dynamic complexities like societal responses muddy the practical interpretation of many estimated parameters. The computer program ARRP, already available from sequence alignment applications, automatically estimated the end of the exponential phase in COVID-19 and extracted the exponential growth rate r for 160 countries. By positing a gamma-distributed generation time, the exponential growth method then yielded R0 estimates for COVID-19 in 160 countries. The use of ARRP ensured that the R0 estimates were largely freed from any dependency outside the exponential phase. The Prem matrices quantify rates of effective contact for infectious disease. Without using any age-stratified COVID-19 data, but under strong assumptions about the homogeneity of susceptibility, infectiousness, etc., across different age-groups, the Prem contact matrices also yielded theoretical R0 estimates for COVID-19 in 152 countries, generally in quantitative conflict with the R0 estimates derived from the exponential growth method. An exploratory analysis manipulating only the Prem contact matrices reduced the conflict, suggesting that age-groups under 20 years did not promote the initial exponential growth of COVID-19 as much as other age-groups. The analysis therefore supports tentatively and tardily, but independently of age-stratified COVID-19 data, the low priority given to vaccinating younger age groups. It also supports the judicious reopening of schools. The exploratory analysis also supports the possibility of suspecting differences in epidemic spread among different age-groups, even before substantial amounts of age-stratified data become available.

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“…One commonly used indicator of epidemic dynamics is the effective reproductive number R t , defined roughly as the expected number of secondary infections caused by a typical infected individual at time t. This number aggregates the factors mentioned above by simultaneously averaging over individuals and individual behaviour. However, the usefulness of this quantity is subject to certain limitations [1] and, since it is defined in terms of a universal average, it is not possible to measure the true R t of a population. Additional simplifying assumptions, on the population and its mixing habits, are required in order that R t be estimated.…”

Section: Introductionmentioning

confidence: 99%

Estimating the impact of interventions against COVID-19: from lockdown to vaccination

Thompson

Wattam²

2021

Preprint

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Coronavirus disease 2019 (COVID-19) is an infectious disease of humans caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since the first case was identified in China in December 2019 the disease has spread worldwide, leading to an ongoing pandemic. In this article, we present a detailed agent-based model of COVID-19 in Luxembourg, and use it to estimate the impact, on cases and deaths, of interventions including testing, contact tracing, lockdown, curfew and vaccination. Our model is based on collation, with agents performing activities and moving between locations accordingly. The model is highly heterogeneous, featuring spatial clustering, over 2000 behavioural types and a 10 minute time resolution. The model is validated against COVID-19 clinical monitoring data collected in Luxembourg in 2020. Our model predicts far fewer cases and deaths than the equivalent equation-based SEIR model. In particular, with $R_0 = 2.45$, the SEIR model infects 87% of the resident population while our agent-based model results, on average, in only around 23% of the resident population infected. Our simulations suggest that testing and contract tracing reduce cases substantially, but are much less effective at reducing deaths. Lockdowns appear very effective although costly, while the impact of an 11pm-6am curfew is relatively small. When vaccinating against a future outbreak, our results suggest that herd immunity can be achieved at relatively low levels, with substantial levels of protection achieved with only 30% of the population immune. When vaccinating in midst of an outbreak, the challenge is more difficult. In this context, we investigate the impact of vaccine efficacy, capacity, hesitancy and strategy. We conclude that, short of a permanent lockdown, vaccination is by far the most effective way to suppress and ultimately control the spread of COVID-19.

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What the reproductive number R0 can and cannot tell us about COVID-19 dynamics

Cited by 34 publications

References 112 publications

A Review of Matrix SIR Arino Epidemic Models

A Review of Matrix SIR Arino Epidemic Models

A comprehensive estimation of country-level basic reproduction numbers R0 for COVID-19: Regime regression can automatically estimate the end of the exponential phase in epidemic data

Estimating the impact of interventions against COVID-19: from lockdown to vaccination

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