Flattening the curve

Measures such as hand washing, social distancing and face masks reduce and delay the peak of active cases, allowing more time for healthcare capacity to increase and better cope with patient load.[1] Time gained through thus flattening the curve can be used to raise the line of healthcare capacity to better meet surging demand.[2]
Without pandemic containment measures—such as social distancing, vaccination, and use of face masks—pathogens can spread exponentially.[3] This graphic illustrates how early adoption of containment measures tends to protect wider swaths of the population, thus reducing and delaying the peak of active cases.
SIR model showing the impact of reducing the infection rate () by 76%

Flattening the curve was a public health strategy to slow down the spread of the SARS-CoV-2 virus during the early stages of the COVID-19 pandemic. The curve being flattened is the epidemic curve, a visual representation of the number of infected people needing health care over time. During an epidemic, a health care system can break down when the number of people infected exceeds the capability of the health care system's ability to take care of them. Flattening the curve means slowing the spread of the epidemic so that the peak number of people requiring care at a time is reduced, and the health care system does not exceed its capacity. Flattening the curve relies on mitigation techniques such as hand washing, use of face masks and social distancing.

A complementary measure is to increase health care capacity, to "raise the line".[4] As described in an article in The Nation, "preventing a health care system from being overwhelmed requires a society to do two things: 'flatten the curve'—that is, slow the rate of infection so there aren't too many cases that need hospitalization at one time—and 'raise the line'—that is, boost the hospital system's capacity to treat large numbers of patients."[5] As of April 2020, in the case of the COVID-19 pandemic, two key measures are to increase the numbers of available ICU beds and ventilators, which are in systemic shortage.[2]

Experts differentiate between "zero-COVID", which is an elimination strategy, and "flattening the curve" a mitigation strategy that attempt to lessen the effects of the virus on society, but which still tolerate some level of transmission within the community.[6][7] These two initial strategies can be pursued sequentially or simultaneously during the acquired immunity phase through natural and vaccine-induced immunity.[8]

Background

Warnings about the risk of pandemics were repeatedly made throughout the 2000s and the 2010s by major international organisations including the World Health Organization (WHO) and the World Bank, especially after the 2002–2004 SARS outbreak.[9] Governments, including those in the United States and France, both prior to the 2009 swine flu pandemic, and during the decade following the pandemic, both strengthened their health care capacities and then weakened them.[10][11] At the time of the COVID-19 pandemic, health care systems in many countries were functioning near their maximum capacities.[4]

In a situation like this, when a sizable new epidemic emerges, a portion of infected and symptomatic patients create an increase in the demand for health care that has only been predicted statistically, without the start date of the epidemic nor the infectivity and lethality known in advance.[4] If the demand surpasses the capacity line in the infections per day curve, then the existing health facilities cannot fully handle the patients, resulting in higher death rates than if preparations had been made.[4]

An influential UK study showed that an unmitigated COVID-19 response in the UK could have required up to 46 times the number of available ICU beds.[12] One major public health management challenge is to keep the epidemic wave of incoming patients needing material and human health care resources supplied in a sufficient amount that is considered medically justified.[4]

Flattening the curve

Queue markers at a shopping mall in Bangkok as a social distancing practicing

Non-pharmaceutical interventions such as hand washing, social distancing, isolation and disinfection[4] reduce the daily infections, therefore flattening the epidemic curve. A successfully flattened curve spreads health care needs over time and the peak of hospitalizations under the health care capacity line.[2] Doing so, resources, be it material or human, are not exhausted and lacking. In hospitals, it for medical staff to use the proper protective equipment and procedures, but also to separate contaminated patients and exposed workers from other populations to avoid intra-hospital spread.[4]

Raising the line

Along with the efforts to flatten the curve is the need for a parallel effort to "raise the line", to increase the capacity of the health care system.[2] Healthcare capacity can be raised by raising equipment, staff, providing telemedicine, home care and health education to the public.[4] Elective procedures can be cancelled to free equipment and staffs.[4] Raising the line aims to provide adequate medical equipment and supplies for more patients.[13]

During the COVID-19 pandemic

Simulations comparing rate of spread of infection, and number of deaths due to overrun of hospital capacity, when social interactions are "normal" (left, 200 people moving freely) and "distanced" (right, 25 people moving freely).
Green = Healthy, uninfected individuals
Red = Infected individuals
Blue = Recovered individual
Black = Dead individuals
[14]

The concept was popular during the early months of the COVID-19 pandemic.[15]

According to Vox, in order to move away from social distancing and return to normal, the US needs to flatten the curve by isolation and mass testing, and to raise the line.[16] Vox encourages building up health care capability including mass testing, software and infrastructures to trace and quarantine infected people, and scaling up cares including by resolving shortages in personal protection equipment, face masks.[16]

According to The Nation, territories with weak finances and health care capacity such as Puerto Rico face an uphill battle to raise the line, and therefore a higher imperative pressure to flatten the curve.[5]

In March 2020, UC Berkeley Economics and Law professor Aaron Edlin commented that ongoing massive efforts to flatten the curve supported by trillions dollars emergency package should be matched by equal efforts to raise the line and increase health care capacity.[17] Edlin called for an activation of the Defense Production Act to order manufacturing companies to produce the needed sanitizers, personal protective equipment, ventilators, and set up hundreds thousands to millions required hospital beds.[17] Standing in March 2020 estimates, Edlin called for the construction of 100-300 emergency hospitals to face what he described as "the largest health catastrophe in 100 years" and to adapt health care legislation preventing emergency practices needed in time of pandemics.[17] Edlin pointed out proposed stimulus package as oriented toward financial panics, while not providing sufficient funding for the core issue of a pandemic: health care capability.[17]

In early May, the senior contributor on healthcare from Forbes posted, "Tenet Healthcare said its more than 60 hospitals are 'not being overwhelmed' by patients sickened by the Coronavirus strain COVID-19, the latest sign the U.S. healthcare system may be effectively coping with the pandemic," suggesting that the goal of flattening the curve to a point below health care capacity had met with initial success.[18] By 2021, the phrase "flatten the curve" had largely fallen out of medical messaging etymology.[19][20]

See also

References

  1. ^ Wiles, Siouxsie (9 March 2020). "The three phases of Covid-19—and how we can make it manageable". The Spinoff. Morningside, Auckland, New Zealand. Archived from the original on 27 March 2020. Retrieved 9 March 2020.
  2. ^ a b c d Barclay, Eliza (7 April 2020). "Chart: The US doesn't just need to flatten the curve. It needs to "raise the line."". Vox. Archived from the original on 7 April 2020. Retrieved 7 April 2020.
  3. ^ Maier, Benjamin F.; Brockmann, Dirk (15 May 2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492): 742–746. Bibcode:2020Sci...368..742M. doi:10.1126/science.abb4557. PMC 7164388. PMID 32269067. ("...initial exponential growth expected for an unconstrained outbreak.")
  4. ^ a b c d e f g h i Beating Coronavirus: Flattening the Curve, Raising the Line (YouTube video). Retrieved 12 April 2020.
  5. ^ a b Gelardi, Chris (9 April 2020). "Colonialism Made Puerto Rico Vulnerable to Coronavirus Catastrophe". The Nation. ISSN 0027-8378. Archived from the original on 12 April 2020. Retrieved 12 April 2020.
  6. ^ Oliu-Barton, Miquel; Pradelski, Bary S R; Aghion, Philippe; Artus, Patrick; Kickbusch, Ilona; Lazarus, Jeffrey V; Sridhar, Devi; Vanderslott, Samantha (28 April 2021). "SARS-CoV-2 elimination, not mitigation, creates best outcomes for health, the economy, and civil liberties". The Lancet. 397 (10291): 2234–2236. doi:10.1016/S0140-6736(21)00978-8. PMC 8081398. PMID 33932328.
  7. ^ Li, Zhongjie; Chen, Qiulan; Feng, Luzhao; Rodewald, Lance; Xia, Yinyin; Yu, Hailiang; Zhang, Ruochen; An, Zhijie; Yin, Wenwu; Chen, Wei; Qin, Ying; Peng, Zhibin; Zhang, Ting; Ni, Daxin; Cui, Jinzhao; Wang, Qing; Yang, Xiaokun; Zhang, Muli; Ren, Xiang; Wu, Dan; Sun, Xiaojin; Li, Yuanqiu; Zhou, Lei; Qi, Xiaopeng; Song, Tie; Gao, George F; Feng, Zijian (4 June 2020). "Active case finding with case management: the key to tackling the COVID-19 pandemic". The Lancet. 396 (10243): 63–70. doi:10.1016/S0140-6736(20)31278-2. PMC 7272157. PMID 32505220.
  8. ^ Bhopal, Raj S (9 September 2020). "To achieve "zero covid" we need to include the controlled, careful acquisition of population (herd) immunity". BMJ. 370: m3487. doi:10.1136/bmj.m3487. eISSN 1756-1833. PMID 32907816. S2CID 221538577.
  9. ^ "Wanted: world leaders to answer the coronavirus pandemic alarm". South China Morning Post. 31 March 2020. Archived from the original on 9 April 2020. Retrieved 6 April 2020.
  10. ^ Manjoo, Farhad (25 March 2020). "Opinion | How the World's Richest Country Ran Out of a 75-Cent Face Mask". The New York Times. ISSN 0362-4331. Archived from the original on 25 March 2020. Retrieved 25 March 2020.
  11. ^ "Pénurie de masques : une responsabilité partagée par les gouvernements" [Lack of masks: a responsibility shared by governments]. Public Senat (in French). 23 March 2020. Archived from the original on 9 April 2020. Retrieved 6 April 2020.
  12. ^ Imperial College COVID-19 Response Team (16 March 2020). "Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand" (PDF). Archived (PDF) from the original on 16 March 2020. Retrieved 23 March 2020 – via imperial.ac.uk.
  13. ^ Dudley, Joshua. "Q&A: Dr. Rishi Desai Talks To Medical Professionals About What We Can Learn From COVID-19". Forbes. Archived from the original on 12 June 2020. Retrieved 18 June 2020.
  14. ^ Stevens, Harry (14 March 2020). "These simulations show how to flatten the coronavirus growth curve". The Washington Post. Archived from the original on 30 March 2020. Retrieved 29 March 2020.
  15. ^ Roberts, Siobhan (27 March 2020). "Flattening the Coronavirus Curve". The New York Times. ISSN 0362-4331. Archived from the original on 11 April 2020. Retrieved 12 April 2020.
  16. ^ a b Lopez, German (10 April 2020). "Why America is still failing on coronavirus testing". Vox.com. Archived from the original on 20 December 2020. Retrieved 12 April 2020.
  17. ^ a b c d Edlin, Aaron (March 2020). "Don't just flatten the curve: Raise the line" (PDF). p. 2. Archived (PDF) from the original on 18 April 2020. Retrieved 12 April 2020 – via berkeley.edu.
  18. ^ Japsen, Bruce (4 May 2020). "Hospital Operator Tenet Healthcare 'Not Overwhelmed' with Coronavirus Cases". Forbes. Archived from the original on 11 May 2020. Retrieved 10 May 2020.
  19. ^ "We haven't failed on the virus". Australian Financial Review. 29 June 2021. Retrieved 2 July 2021.
  20. ^ Scott, Dylan (31 December 2020). "Flattening the curve worked — until it didn't". Vox. Retrieved 2 July 2021.

Media files used on this page

SARS-CoV-2 (Wikimedia colors).svg
Author/Creator: Geraki, Licence: CC BY-SA 4.0
SARS-CoV-2 logo in Wikimedia colors
Queue during COVID-19 must be social distancing at ICONSIAM.jpg
Author/Creator: Chainwit., Licence: CC BY-SA 4.0
Queuing markers to separate customers from each other as a social distancing policy of ICONSIAM shopping complex in Bangkok
SIR model anim.gif
Author/Creator: Phrontis, Licence: CC BY-SA 3.0
Animation of the SIR model with initial values , , , and rate of recovery . The animation shows the effect of reducing the rate of infection from to . If there is no medicine or vaccination available, it is only possible to reduce the infection rate (often referred to as "flattening the curve") by appropriate measures such as social distancing. System of differential equations used for this model:

This animation was created with GeoGebra by computing the numerical solutions of the system of differential equations. The core part of the construction is as follows:

####################################
# system of differential equations #
####################################
S'(t, S, I, R) = -ß I S
I'(t, S, I, R) = ß S I - γ I
R'(t, S, I, R) = γ I

###############################################################
# numerical solutions of the system of differential equations #
###############################################################
NSolveODE[{S', I', R'}, 0, {s_0, i_0, r_0}, T_{max}]

# Result:
# numericalIntegral1 -> S
# numericalIntegral2 -> I
# numericalIntegral3 -> R

Note: Some authors use modified, but equivalent forms of the ODEs. Unfortunately, the same parameters are sometimes used. Example for the first ODE, where the infection rate is named for the sake of clarity:

By substituting , you get the same ODE as above. is a constant value (invariant of the model) and not needed for the ODE; in fact, the implementation didn't even use a variable for .
20200403 Flatten the curve animated GIF.gif
Author/Creator: RCraig09, Licence: CC BY-SA 4.0
Animated graphic showing "flattening the curve" by slowing the spread of pandemics such as Coronavirus, so that health care demands stay within capacity.

Designer's note:

  • An "international" version, without text, is shown and linked below.
  • Graphic was made in response to a request at Commons:Graphic Lab/Illustration workshop (diff).
  • I made 49 individual graphic frames manually with Inkskape (esp. its Bezier tool) and exported as 49 unique PNGs. I imported the 49 PNGs as layers into Gimp. To pad the beginning and end with a "stationary" intro and finish, I added about 33 extra first and last frames within Gimp before exporting as a 30 ms/frame GIF.
  • Example of visualizing changing healthcare capacity (sloping dashed line) is found at:
Radtke, Alexander Flatten the coronavirus curve. FlowingData.com. Nathan Yau (editor) (March 9, 2020). Archived from the original on March 12, 2020.
  • Symbols make the graphic friendlier for an international audience.
Katapult importance social distancing.gif
(c) Katapult Magazin, CC BY-SA 4.0
Simulation of the effect of social distancing with 200 vs 25 individuals moving freely.
20200609 Effect of pandemic containment measures.gif
Author/Creator: RCraig09, Licence: CC BY-SA 4.0
Animated GIF showing pathogen propagation in the absence of, and in the presence of, pandemic containment measures.
  • Suggested caption: Without pandemic containment measures—such as social distancing, vaccination, and use of face masks—pathogens can spread exponentially.[source] This graphic shows how early adoption of containment measures tends to protect wider swaths of the population.
  • Suggested source for caption: Maier, Benjamin F., Brockmann, Dirk, (15 May 2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science 368 (6492): 742-746. DOI:10.1126/science.abb4557. ("...initial exponential growth expected for an unconstrained outbreak.")
  • Wikitext for citation: <ref name=Science_20200515>{{cite journal |last1=Maier |first1=Benjamin F. |last2=Brockmann |first2=Dirk |title=Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China |journal=Science |date=15 May 2020 |volume=368 |issue=6492 |pages=742-746 |doi=10.1126/science.abb4557 |url=https://science.sciencemag.org/content/368/6492/742}} ("...initial exponential growth expected for an unconstrained outbreak.")</ref>
  • Animation is designed to be consistent with the pandemic-related GIFs shown below.