scholarly journals Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China

Science ◽  
2020 ◽  
Vol 368 (6492) ◽  
pp. 742-746 ◽  
Author(s):  
Benjamin F. Maier ◽  
Dirk Brockmann
Keyword(s):  
Exponential Growth ◽  
Early Phase ◽  
Mainland China ◽  
Direct Consequence ◽  
Growth Behavior ◽  
Behavioral Changes ◽  
Susceptible Population ◽  
Subexponential Growth ◽  
Recent Outbreak ◽  
Parsimonious Model

The recent outbreak of coronavirus disease 2019 (COVID-19) in mainland China was characterized by a distinctive subexponential increase of confirmed cases during the early phase of the epidemic, contrasting with an initial exponential growth expected for an unconstrained outbreak. We show that this effect can be explained as a direct consequence of containment policies that effectively deplete the susceptible population. To this end, we introduce a parsimonious model that captures both quarantine of symptomatic infected individuals, as well as population-wide isolation practices in response to containment policies or behavioral changes, and show that the model captures the observed growth behavior accurately. The insights provided here may aid the careful implementation of containment strategies for ongoing secondary outbreaks of COVID-19 or similar future outbreaks of other emergent infectious diseases.

scholarly journals Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 outbreak in Mainland China

2020 ◽  
Author(s):  
Benjamin F. Maier ◽  
Dirk Brockmann
Keyword(s):  
Exponential Growth ◽  
Scaling Law ◽  
Mainland China ◽  
Direct Consequence ◽  
Behavioral Changes ◽  
Reproduction Rate ◽  
Susceptible Population ◽  
Wide Range ◽  
Recent Outbreak ◽  
Parsimonious Model

The recent outbreak of COVID-19 in Mainland China is characterized by a distinctive algebraic, sub-exponential increase of confirmed cases with time during the early phase of the epidemic, contrasting an initial exponential growth expected for an unconstrained outbreak with sufficiently large reproduction rate. Although case counts vary significantly between affected provinces in Mainland China, the scaling law tμ is surprisingly universal, with a range of exponents μ = 2.1 ± 0.3. The universality of this behavior indicates that, in spite of social, regional, demographical, geographical, and socio-economical heterogeneities of affected Chinese provinces, this outbreak is dominated by fundamental mechanisms that are not captured by standard epidemiological models. We show that the observed scaling law is a direct consequence of containment policies that effectively deplete the susceptible population. To this end we introduce a parsimonious model that captures both, quarantine of symptomatic infected individuals as well as population wide isolation in response to mitigation policies or behavioral changes. For a wide range of parameters, the model reproduces the observed scaling law in confirmed cases and explains the observed exponents. Quantitative fits to empirical data permit the identification of peak times in the number of asymptomatic or oligo-symptomatic, unidentified infected individuals, as well as estimates of local variations in the basic reproduction number. The model implies that the observed scaling law in confirmed cases is a direct signature of effective contaiment strategies and/or systematic behavioral changes that affect a substantial fraction of the susceptible population. These insights may aid the implementation of containment strategies in potential export induced COVID-19 secondary outbreaks elsewhere or similar future outbreaks of other emergent infectious diseases.

scholarly journals Modeling Growth, Containment and Decay of the COVID-19 Epidemic in Italy

2020 ◽  
Vol 8 ◽  
Author(s):  
Francesco Capuano
Keyword(s):  
Exponential Growth ◽  
Compartment Model ◽  
Growth Behavior ◽  
Time Dependent ◽  
Model Parameters ◽  
Susceptible Population ◽  
Dependent Rate ◽  
Slow Decay ◽  
Cumulative Curve ◽  
Modeling Growth

A careful inspection of the cumulative curve of confirmed COVID-19 infections in Italy and in other hard-hit countries reveals three distinct phases: i) an initial exponential growth (unconstrained phase), ii) an algebraic, power-law growth (containment phase), and iii) a relatively slow decay. We propose a parsimonious compartment model based on a time-dependent rate of depletion of the susceptible population that captures all such phases for a plausible range of model parameters. The results suggest an intimate interplay between the growth behavior, the timing and implementation of containment strategies, and the subsequent saturation of the outbreak.

Exponential Growth in San Juan Basin Fruitland Coalbed Permeability With Reservoir Drawdown: Model Match and New Insights

2010 ◽  
Vol 13 (06) ◽  
pp. 914-925 ◽  
Author(s):  
J.-Q.. -Q. Shi ◽  
S.. Durucan
Keyword(s):  
Exponential Growth ◽  
Growth Behavior ◽  
San Juan ◽  
Reservoir Pressure ◽  
Permeability Model ◽  
Matrix Shrinkage ◽  
San Juan Basin ◽  
Volume Compressibility ◽  
Stress Dependent ◽  
Permeability Data

Summary The exponential-growth behavior of coalbed permeability with reservoir pressure depletion has been observed previously at the Fairway wells in the San Juan basin. More recently, the exponential trend has also been confirmed for a group of 10 wells in a region northeast of Fairway. Increase in the absolute permeability of coalbeds is a result of matrix shrinkage caused by gas desorption, which becomes a dominant factor on cleat permeability over the effective-stress effect during reservoir production. A permeability model previously developed by the authors has been revisited in an effort to match the recently published field-permeability data. The Shi and Durucan (S&D) permeability model (2004, 2005a) makes use of a stress permeability relationship reported in the literature for an idealized geometry (matchsticks), in which the permeability varies exponentially with changes in the effective horizontal stress through the use of a constant cleat (pore) compressibility parameter. In this study, a stress-dependent cleat volume compressibility defined by an initial compressibility with a negative exponential decline rate was adopted. By tuning these two parameters, it was possible to achieve a close match to all the field-permeability data by use of a common set of reservoir properties (elastic properties and matrix-shrinkage parameters) that are consistent with the available field and laboratory data in the literature. The matching of the field-permeability data in these two regions of the San Juan basin in this study has further validated the updated S&D permeability model (now with variable cleat-volume compressibility). It has also provided theoretical support for the observed near-exponential growth behavior of coalbed permeability in a producing reservoir. Furthermore, the model has shed new light on the permeability behavior: (1) The exponential growth occurs when the reservoir pressure is reduced to a level generally below the permeability-recovery pressure (the reservoir pressure at which the initial permeability is recovered); (2) The reservoir permeability in these two regions would remain relatively flat at reservoir pressures above the permeability recovery pressure.

scholarly journals Combinatorics Meets Potential Theory

10.37236/5877 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Philippe D'Arco ◽  
Valentina Lacivita ◽  
Sami Mustapha
Keyword(s):  
Potential Theory ◽  
Generating Functions ◽  
Exponential Growth ◽  
Golden Ratio ◽  
Two Dimensions ◽  
Infinite Group ◽  
Zero Drift ◽  
Small Step ◽  
Subexponential Growth

Using potential theoretic techniques, we show how it is possible to determine the dominant asymptotics for the number of walks of length $n$, restricted to the positive quadrant and taking unit steps in a balanced set $\Gamma$. The approach is illustrated through an example of inhomogeneous space walk. This walk takes its steps in $\{ \leftarrow, \uparrow, \rightarrow, \downarrow \}$ or $\{ \swarrow, \leftarrow, \nwarrow, \uparrow,\nearrow, \rightarrow, \searrow, \downarrow \}$, depending on the parity of the coordinates of its positions. The exponential growth of our model is $(4\phi)^n$, where $\phi= \frac{1+\sqrt 5}{2}$denotes the Golden ratio, while the subexponential growth is like $1/n$.As an application of our approach we prove the non-D-finiteness in two dimensions of the length generating functions corresponding to nonsingular small step sets with an infinite group and zero-drift.

scholarly journals A data-driven assessment of early travel restrictions related to the spreading of the novel COVID-19 within mainland China

2020 ◽  
Author(s):  
Alberto Aleta ◽  
Qitong Hu ◽  
Jiachen Ye ◽  
Peng Ji ◽  
Yamir Moreno
Keyword(s):  
Mainland China ◽  
Behavioral Changes ◽  
The Novel ◽  
Metapopulation Model ◽  
Short Term ◽  
Effective Measure ◽  
Mobility Data ◽  
Health Authorities ◽  
Travel Restrictions ◽  
Novel Coronavirus

Two months after it was firstly reported, the novel coronavirus disease COVID-19 has already spread worldwide. However, the vast majority of reported infections have occurred in China. To assess the effect of early travel restrictions adopted by the health authorities in China, we have implemented an epidemic metapopulation model that is fed with mobility data corresponding to 2019 and 2020. This allows to compare two radically different scenarios, one with no travel restrictions and another in which mobility is reduced by a travel ban. Our findings indicate that i) travel restrictions are an effective measure in the short term, however, ii) they are ineffective when it comes to completely eliminate the disease. The latter is due to the impossibility of removing the risk of seeding the disease to other regions. Our study also highlights the importance of developing more realistic models of behavioral changes when a disease outbreak is unfolding.

scholarly journals Japanese citizens' behavioral changes and preparedness against COVID-19: An online survey during the early phase of the pandemic

PLoS ONE ◽  
2020 ◽  
Vol 15 (6) ◽  
pp. e0234292 ◽  
Author(s):  
Kaori Muto ◽  
Isamu Yamamoto ◽  
Miwako Nagasu ◽  
Mikihito Tanaka ◽  
Koji Wada
Keyword(s):  
Early Phase ◽  
Online Survey ◽  
Behavioral Changes

The Problem of Changing Language Communities: Veterans and Memory Writing in China, Taiwan, and Japan

2011 ◽  
Vol 45 (2) ◽  
pp. 399-429 ◽  
Author(s):  
AARON WILLIAM MOORE
Keyword(s):  
Historical Memory ◽  
Mainland China ◽  
Direct Consequence ◽  
Oral Histories ◽  
Language Community ◽  
Literary Works ◽  
Testimonial Literature ◽  
Community Or ◽  
Post War ◽  
With Memory

AbstractThis paper examines the role that veterans played in the construction of historical memory narratives in mainland China, Taiwan, and Japan. I argue that veterans, who had long established a ‘language community’ with a particular way to speak about the war, found it difficult to communicate with post-war audiences that did not share that experience. The paper analyses six categories of ‘memory writing’ that veterans used to engage with memory debates: post-war diaries, ‘testimonial literature’, articles and literary works, surveys and oral histories, memoirs, and paratext. This study thus proposes that veterans do not avoid discussion of war, but can only be ‘heard’ by members of their language community, or by a post-war society that is prepared to ‘listen’ to their message with little mediation. This is a direct consequence of their experience of the war, and how they crafted their language community at that time.

scholarly journals Characterizing the reproduction number of epidemics with early subexponential growth dynamics

2016 ◽  
Vol 13 (123) ◽  
pp. 20160659 ◽  
Author(s):  
Gerardo Chowell ◽  
Cécile Viboud ◽  
Lone Simonsen ◽  
Seyed M. Moghadas
Keyword(s):  
Growth Model ◽  
Exponential Growth ◽  
Reproduction Number ◽  
Growth Dynamics ◽  
Accurate Estimation ◽  
Rapid Decline ◽  
Spatial Effects ◽  
Emerging Infections ◽  
Subexponential Growth ◽  
Analytical Results

Early estimates of the transmission potential of emerging and re-emerging infections are increasingly used to inform public health authorities on the level of risk posed by outbreaks. Existing methods to estimate the reproduction number generally assume exponential growth in case incidence in the first few disease generations, before susceptible depletion sets in. In reality, outbreaks can display subexponential (i.e. polynomial) growth in the first few disease generations, owing to clustering in contact patterns, spatial effects, inhomogeneous mixing, reactive behaviour changes or other mechanisms. Here, we introduce the generalized growth model to characterize the early growth profile of outbreaks and estimate the effective reproduction number, with no need for explicit assumptions about the shape of epidemic growth. We demonstrate this phenomenological approach using analytical results and simulations from mechanistic models, and provide validation against a range of empirical disease datasets. Our results suggest that subexponential growth in the early phase of an epidemic is the rule rather the exception. Mechanistic simulations show that slight modifications to the classical susceptible–infectious–removed model result in subexponential growth, and in turn a rapid decline in the reproduction number within three to five disease generations. For empirical outbreaks, the generalized-growth model consistently outperforms the exponential model for a variety of directly and indirectly transmitted diseases datasets (pandemic influenza, measles, smallpox, bubonic plague, cholera, foot-and-mouth disease, HIV/AIDS and Ebola) with model estimates supporting subexponential growth dynamics. The rapid decline in effective reproduction number predicted by analytical results and observed in real and synthetic datasets within three to five disease generations contrasts with the expectation of invariant reproduction number in epidemics obeying exponential growth. The generalized-growth concept also provides us a compelling argument for the unexpected extinction of certain emerging disease outbreaks during the early ascending phase. Overall, our approach promotes a more reliable and data-driven characterization of the early epidemic phase, which is important for accurate estimation of the reproduction number and prediction of disease impact.

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