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Modelovanje epidemije i dugoročne procene njenog kretanja


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Statement of the German Society for Epidemiology (DGEpi) on the spread of the new coronavirus (SARS-CoV-2)

 

Background

In December 2019, an outbreak of coronavirus 2 (SARS-CoV-2) occurred in Wuhan, a city in China with 11 million inhabitants. The virus has spread throughout China and beyond. On 12 February 2020, the World Health Organization (WHO) officially named the disease caused by the novel coronavirus Coronavirus Disease 2019 (COVID-19). On 11 March 2020, the WHO declared a pandemic.

 

Aim of the statement

Our aim is to evaluate the current situation and the available findings from an epidemiological perspective and to provide an assessment of future developments and necessary measures. For this purpose, mathematical models of the further spread of infection are presented. Due to the currently still limited knowledge on the behaviour of SARS-CoV-2, the results of the modelling are subject to numerous uncertainties. Within the framework of the models, however, a broad spectrum of possible developments and the effect of infection control measures can be presented in an orienting manner. These models are suitable for deriving current recommendations for infection control.

 

Clinical appearance, distribution

In order to make predictions, it is necessary in the current situation to make assumptions about the behaviour of the infectious agent. These are based on data on the occurrence of the infection observed to date and become increasingly predictable the longer the pandemic lasts. Published data suggest that infections with SARS-CoV-2 are mild to moderate in most cases, while 2-6% of cases require treatment in intensive care units.

Risk groups for severe courses are mainly elderly people [1, 2] and people with previous illnesses. Tobacco use also appears to be a risk factor for an unfavourable course of the disease [1]. Children usually have a very mild course, but can still transmit the infection. An important parameter for modelling the spread of infection is the baseline reproduction rate (R0). This indicates the average number of people infected by an infected person if no infection control measures are taken and there is no immunity in the population (this changes as the infection spreads and is referred to as the effective reproduction rate). For SARS-CoV-2, R0 is estimated at 2-3 [3]. In a scenario where NO specific control measures are implemented and no spontaneous behavioural changes occur, assuming that all individuals develop immune protection after infection, about 50-70% of the population would become infected during the course of the outbreak, initially at an exponentially increasing rate. If the epidemic were to proceed unhindered according to this scenario, the peak of the outbreak (maximum number of infected persons) would already be in spring/summer 2020 (Fig. 1).

The different curves in the graph also show slower progression of the epidemic, i.e. they show what happens when the reproduction rate is reduced by the introduction of control measures, as currently already partially implemented in Germany. The great danger of an unimpeded outbreak is that a very large number of patients would require treatment in intensive care units in a short period of time and the health system would very quickly be overwhelmed by this. Currently, the health care system in Germany has about 30,000 intensive care beds; most of these are needed on an ongoing basis for patients who require intensive care regardless of the current COVID-19 problem. When interpreting the model results, it is noticeable that even moderately slowed progression of the infection spread would lead to decompensation of the health care system. Only a reduction of the effective reproductive rate to a range very close to 1 (1 to 1.2) would enable a course within the existing capacities of the health care system. Controlling the speed of propagation into this narrow range seems practically inconceivable, because even a small increase in the reproductive rate would lead to the health care system being overtaxed.

Another possible strategy would be to reduce the effective reproductive rate below 1 and thus contain the epidemic. The decisive measure here is, in addition to the already established infection control strategies (e.g. reduction of the probability of transmission by consistent hand hygiene, isolation of infected persons, quarantine of contact persons), to achieve a restriction of social contacts to the bare minimum in the entire population. If it is possible to contain the spread of infection in Germany in this way until there are no new cases, the introduction of the infection must continue to be prevented, or individual cases that occur must be quickly identified and isolated using a broad-based testing strategy.

Figs. 2a and 2b show in more detail the great effect of the time of the beginning of containment on the further course of the spread and the necessary resources. We assume that the measures taken so far have already brought about a reduction in the effective reproduction rate; the extent is not clear. Therefore, an infection spread is shown that continues from 15 March with the effective reproduction rate of 1.5 or 2 and 5 scenarios with further contact-reducing measures 7, 14, 21, 28 or 35 days later are introduced. The scenarios show that additional measures would have to be introduced within the next two weeks in order not to exceed the capacity of intensive care units. It is also likely that these cuts would have to be maintained over the next few months in order to completely contain the spread of infection.

Currently, there is a short time window in which the decision between containing or slowing down the spread of infection can be made without overburdening the health care system. In both cases, consistent implementation is necessary for a longer period of time.

Since there is currently no causal therapy or preventive vaccination, it is important in the current epidemiological situation to convince the population to contribute voluntarily and consistently to limiting transmission. Although not all regions of Germany are equally affected at present, it is necessary to implement appropriate spread-limiting measures everywhere as a precautionary measure.

We support the measures that have already been implemented by the Federal Government and we urge that the implementation of further measures be critically reviewed. We should always be aware that these restrictions on civil rights represent a considerable human, social, economic and also health-related burden for the people and companies in our country. It is therefore necessary that a public debate be held on these issues - in full knowledge of the different scenarios, the impending dangers and our own possibilities. A continuous assessment and evaluation of the situation will continue to be necessary.

 

Version from 21.03.2020

 

The modelling of the course of the epidemic is based on a SEIR model with the following parameters: pre-infectious time - 5.5 days, infectious time - 3 days, 2-6% of all infected persons need intensive care with a delay of 10 days and an intensive care period of 10-20 days. At time 0 (start of measures) 40,000 persons are already infected but have no symptoms and are not contagious for the others, 10,000 persons are infectious. Some of the persons may (still) be asymptomatic. The infectious persons are not necessarily all tested - to compare this number with the confirmed cases, one would have to make an assumption about how fully they are tested)

 

https://www.dgepi.de/assets/Stellungnahmen/Stellungnahme2020Corona_DGEpi-21032020.pdf (translation by Deepl)

 

Slike u spoileru:

 

Slika 1:

 

 


Fig. 1: Chronological course of the epidemic for different basic reproduction figures (R0)/effective reproduction figures, different proportions of persons requiring intensive care and length of stay in intensive care units. This represents the effects of control measures through different reproduction numbers after the introduction of the measures on the COVID-19 case numbers. The horizontal axis shows the time and the vertical axis shows the number of persons who are infectious or need intensive care at any one time.

 

pZqenGT.png

 

Prvi grafik:
Naslov i y osa: broj zaraženih
X osa: vreme (u danima)

 

Ostali grafici:
Naslov: x% pacijenata za koje je potrebna intenzivna nega uz ležanje od y dana
Y osa: broj osoba na intenzivnoj nezi
X osa: vreme (u danima)
 

 

Slika 2a:

 

 


Fig. 2a. Further course of the epidemic if measures are taken at different times to reduce the effective reproduction rate below 1. In the model, a reduction of the reproduction number from initially 2 to 0.9 was assumed after 7 days, 14 days, 21 days, 28 days and 35 days. The horizontal axis shows the time and the vertical axis shows the number of persons who are infectious or need intensive care at any one time.

 

rvzcgJt.png

 

Prvi grafik:
Naslov i y osa: broj zaraženih
X osa: vreme (u danima)

 

Ostali grafici:
Naslov: x% pacijenata za koje je potrebna intenzivna nega uz ležanje od y dana
Y osa: broj osoba na intenzivnoj nezi
X osa: vreme (u danima)
 

 

Slika 2b:

 

 


Figure 2b. Further course of the epidemic if measures are taken at different times to reduce the effective reproduction rate below 1. In the model, a reduction of the reproduction number from initially 1.5 to 0.9 was assumed after 7 days, 14 days, 21 days, 28 days and 35 days. The horizontal axis shows the time and the vertical axis shows the number of persons who are infectious or need intensive care at any one time.

 

PLXC0it.png

 

Prvi grafik:
Naslov i y osa: broj zaraženih
X osa: vreme (u danima)

 

Ostali grafici:
Naslov: x% pacijenata za koje je potrebna intenzivna nega uz ležanje od y dana
Y osa: broj osoba na intenzivnoj nezi
X osa: vreme (u danima)

 

 

Kome trebaju veći grafici, može da ih otvori na novom tabu ili da otvori gornji PDF.

Edited by vememah
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Juce su ovde kacene projekcije o 40 - 50 000 mogucih smrti u Spaniji u narednih 12 nedelja. Ovde je krenulo ludjenje i sizenje, gde ce svi ti ljudi da se sahrane, bicemo zatrpani lesevima i sl . Bez imalo zelje da relativizujem opasnost od virusa, taj broj treba staviti u kontekst. Godisnje u Spaniji umre oko pola miliona ljudi. Na tri meseca, bez korone, smrtnost je oko 120 000. Naravno, 30% vise jeste ogroman broj, svakog od njih pojedinacno mi je zao, i mladih i starih, i onih koji bi ziveli jos pola veka, i onih koji bi umrli ove nedelje i bez virusa. Ali nije da ce zemlja od 46 M ljudi ostati pusta ko sela na Staroj planini, ili da ce se praviti masovne grobnice za umrle od korone. Strasnih sam se gluposti naslusao.

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5 minutes ago, chandra said:

Juce su ovde kacene projekcije o 40 - 50 000 mogucih smrti u Spaniji u narednih 12 nedelja. Ovde je krenulo ludjenje i sizenje, gde ce svi ti ljudi da se sahrane, bicemo zatrpani lesevima i sl . Bez imalo zelje da relativizujem opasnost od virusa, taj broj treba staviti u kontekst. Godisnje u Spaniji umre oko pola miliona ljudi. Na tri meseca, bez korone, smrtnost je oko 120 000. Naravno, 30% vise jeste ogroman broj, svakog od njih pojedinacno mi je zao, i mladih i starih, i onih koji bi ziveli jos pola veka, i onih koji bi umrli ove nedelje i bez virusa. Ali nije da ce zemlja od 46 M ljudi ostati pusta ko sela na Staroj planini, ili da ce se praviti masovne grobnice za umrle od korone. Strasnih sam se gluposti naslusao.

 Ovo povecanje od 30% je skuceno u 12 sedmica a ne u 52 sedmice. To jeste problem kao i sa zdracstvenim sistemom.

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12 minutes ago, chandra said:

Juce su ovde kacene projekcije o 40 - 50 000 mogucih smrti u Spaniji u narednih 12 nedelja. Ovde je krenulo ludjenje i sizenje, gde ce svi ti ljudi da se sahrane, bicemo zatrpani lesevima i sl . Bez imalo zelje da relativizujem opasnost od virusa, taj broj treba staviti u kontekst. Godisnje u Spaniji umre oko pola miliona ljudi. Na tri meseca, bez korone, smrtnost je oko 120 000. Naravno, 30% vise jeste ogroman broj, svakog od njih pojedinacno mi je zao, i mladih i starih, i onih koji bi ziveli jos pola veka, i onih koji bi umrli ove nedelje i bez virusa. Ali nije da ce zemlja od 46 M ljudi ostati pusta ko sela na Staroj planini, ili da ce se praviti masovne grobnice za umrle od korone. Strasnih sam se gluposti naslusao.

 

hm ... sizenje nece doprineti resenju

nece se broj regularno umrlih smanjiti pojavom korone bas kao sto bi neki sto ce umreti od korone umrli i ovako, vec ce se verovatno povecati, zbog korone, indirektno

tako da ... sizenje i panika ne, ali discplina i promena navika svakako

sto pre se vratimo u kakvu/takvu normalu, bolje za nas

Edited by cedo
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12 minutes ago, borris_ said:

 Ovo povecanje od 30% je skuceno u 12 sedmica a ne u 52 sedmice. To jeste problem kao i sa zdracstvenim sistemom.

Takodje pitanje je koliko se poklapaju ta dva spiska: umrlih od covida i koji bi svakako umrli u 2020.

Edited by Friend
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1 hour ago, chandra said:

Juce su ovde kacene projekcije o 40 - 50 000 mogucih smrti u Spaniji u narednih 12 nedelja. Ovde je krenulo ludjenje i sizenje, gde ce svi ti ljudi da se sahrane, bicemo zatrpani lesevima i sl . Bez imalo zelje da relativizujem opasnost od virusa, taj broj treba staviti u kontekst. Godisnje u Spaniji umre oko pola miliona ljudi. Na tri meseca, bez korone, smrtnost je oko 120 000. Naravno, 30% vise jeste ogroman broj, svakog od njih pojedinacno mi je zao, i mladih i starih, i onih koji bi ziveli jos pola veka, i onih koji bi umrli ove nedelje i bez virusa. Ali nije da ce zemlja od 46 M ljudi ostati pusta ko sela na Staroj planini, ili da ce se praviti masovne grobnice za umrle od korone. Strasnih sam se gluposti naslusao.

 

 

Te projekcije su zeznuta stvar.

 

Eto baš jutros u u danšnjem NRC-u čitam članak o matematičkom modeliranju širenja infekcija.


Razgovarali su sa nekoliko vodećih stručnjaka. To su simulacije da zaboli glava (tojest trokiraju kompjuteri).


Treba voditi računa o različitim vidovima kretanja i kontakta ljudi različitih zanimanja i starosnih grupa, prijemčivosti na zarazu, trajanju perioda kada je neko zarazan, procentu ljudi koji malaksaju i prestanu da se kreću jer su zaraženi, uticaju međugradskog saobraćaja, opštoj kondiciji različitih grupa stanovnika (po godištu, zanimanju, kondiciji itd)... ludilo.  Da ne nabrajam dalje. Izuzetno složena matematika.


Ima mnogo neočekivanih "pragova", efekata koji sami sebe ubrzavaju ili usporavaju, međuzavisanih parametara...


Često se pojavljuju kontraintuitivni rezultati, kao na primer kada su pre nekoliko godina videli da je bolje ne vakcinisati protiv rubeole nego vakcinisati premali deo populacije...


Ova  odeljenja na fakultetima i institutima za zdravstvo (među kojima je i RIVM, koji savetuje vladu) rintaju prekovremeno. Počeli su još  januara, kada je postalo jasno da u Vuhanu opasno ne valja i kada su se pojavile vesti o privimm zaraženim u Japanu i na Tajlandu.

 

 

One računice na poleđini kafanskog podmetača za pivsku čašu, koje se šire po društvenim mrežama su neozbiljne i ili šire paniku ili zanemaruju opasnost, u zavisnosti od toga šta se autoru tweeta više sviđa.


Čak i modeli iz veterinarske infektologije (zaraze živine i stoke) su matematički gadno zajebani, iako je kretanje domaćih životinja strogo kontrolisano i ograničeno...


Ljudsko društvo je daleko složenije i to na mnogo više nivoa.

 

Ono što je najveći problem je što još uvek ne znamo koliko dugo su nosioci zarazni, koliki procenat ljudi ima kakve simptome, a ni koliko lako se virus prenosi. Procene na osnovu podataka iz različitih država jako variraju.

Edited by Yossarian
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Zaključci iz izveštaja londonskog Imperijal koledža o proceni efikasnosti i posledica dvaju puteva rešavanja krize (prvi - čekanje da se napravi imunitet stada tj. mitigacija i drugi - potpuno potiskivanje zaraze):

Quote

Perhaps our most significant conclusion is that mitigation is unlikely to be feasible without emergency surge capacity limits of the UK and US healthcare systems being exceeded many times over. In the most effective mitigation strategy examined, which leads to a single, relatively short epidemic (case isolation, household quarantine and social distancing of the elderly), the surge limits for both general ward and ICU beds would be exceeded by at least 8-fold under the more optimistic scenario for critical care requirements that we examined. In addition, even if all patients were able to be treated, we predict there would still be in the order of 250,000 deaths in GB, and 1.1-1.2 million in the US. 

In the UK, this conclusion has only been reached in the last few days, with the refinement of estimates of likely ICU demand due to COVID-19 based on experience in Italy and the UK (previous planning estimates assumed half the demand now estimated) and with the NHS providing increasing certainty around the limits of hospital surge capacity.

We therefore conclude that epidemic suppression is the only viable strategy at the current time. The social and economic effects of the measures which are needed to achieve this policy goal will be profound. Many countries have adopted such measures already, but even those countries at an earlier stage of their epidemic (such as the UK) will need to do so imminently.

https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf

Edited by vememah
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Nakon ovog izveštaja, Džonson se konačno uzeo u pamet i počeo da primenjuje neke ozbiljnije mere.

 

Vrlo je žalosno je što Nemci i Englezi tek posle ovoliko vremena dolaze do istih zaključaka do kojih su Kinezi došli još u januaru, a to je da je virus previše zarazan i rezultuje prevelikim brojem teških slučajeva da bi smelo da se dopusti da se u relativno kratkom roku zarazi značajan deo populacije jer kapaciteti nijednog zdravstvenog sistema na svetu to jednostavno ne mogu da izdrže.

Edited by vememah
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Sa Guardianovog live bloga:

 

Quote

It took 67 days from the first reported case to reach the first 100,000 cases of Covid-19, but it took only 11 days for the second 100,000 cases, and just four days for the third 100,000 cases, WHO director general Tedros Adhanom Ghebreyesus, said.

 

:ph34r:

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cuj 67 dana proslo ... i on je glup ... verovatno i uzme neki dinar kao sef whoa, al je glup ko k...c ... tko li mu pise te umotvorine

naime ... kina je zajebala sve glupake ovoga sveta svojom reakcijom kada su shvatili sa cim imaju posla

proslo bi upravo 18 dana do ~100k , a 25 do prvog miliona da nisu nista preduzeli ... da su sedeli ko evropa 40ak dana imali bi oko 180 miliona

i to sve sa 40% prirastom dnevno ... a znamo da danas gledamo i veci

 

edit: i da dodamo da bi se jos i ranije razmileli po svetu

 

 

Edited by cedo
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Quote

In short, the best intervention approach identified by AceMod is to combine restrictions on international arrivals (already implemented in Australia), case isolation (also already implemented to a reasonable extent, but demanding increasing testing and monitoring resources), and social distancing with at least 80%–90% compliance and a duration of 91 days (13 weeks).

 

Modelling transmission and control of the COVID-19 pandemic in Australia 

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Naučnici s Oksforda suprotstavljaju se modelu londonskog Imperijal koledža tvrdeći da ogromna većina zaraženih ne pokazuje nikakve ili skoro nikakve simptome i da je dosad zaražena možda čak polovina britanske populacije i traže da se serološkim ispitivanjima utvrdi stvarno stanje epidemije.

Quote

Coronavirus may have infected half of UK population — Oxford study

New epidemiological model suggests the vast majority of people suffer little or no illness

The new coronavirus may already have infected far more people in the UK than scientists had previously estimated — perhaps as much as half the population — according to modelling by researchers at the University of Oxford.

If the results are confirmed, they imply that fewer than one in a thousand of those infected with Covid-19 become ill enough to need hospital treatment, said Sunetra Gupta, professor of theoretical epidemiology, who led the study. The vast majority develop very mild symptoms or none at all.

“We need immediately to begin large-scale serological surveys — antibody testing — to assess what stage of the epidemic we are in now,” she said.

The modelling by Oxford’s Evolutionary Ecology of Infectious Disease group indicates that Covid-19 reached the UK by mid-January at the latest. Like many emerging infections, it spread invisibly for more than a month before the first transmissions within the UK were officially recorded at the end of February.

The research presents a very different view of the epidemic to the modelling at Imperial College London, which has strongly influenced government policy. “I am surprised that there has been such unqualified acceptance of the Imperial model,” said Prof Gupta. 

However, she was reluctant to criticise the government for shutting down the country to suppress viral spread, because the accuracy of the Oxford model has not yet been confirmed and, even if it is correct, social distancing will reduce the number of people becoming seriously ill and relieve severe pressure on the NHS during the peak of the epidemic.

The Oxford study is based on a what is known as a “susceptibility-infected-recovered model” of Covid-19, built up from case and death reports from the UK and Italy. The researchers made what they regard as the most plausible assumptions about the behaviour of the virus.

The modelling brings back into focus “herd immunity”, the idea that the virus will stop spreading when enough people have become resistant to it because they have already been infected. The government abandoned its unofficial herd immunity strategy — allowing controlled spread of infection — after its scientific advisers said this would swamp the National Health Service with critically ill patients. 

But the Oxford results would mean the country had already acquired substantial herd immunity through the unrecognised spread of Covid-19 over more than two months. If the findings are confirmed by testing, then the current restrictions could be removed much sooner than ministers have indicated.

Although some experts have shed doubt on the strength and length of the human immune response to the virus, Prof Gupta said the emerging evidence made her confident that humanity would build up herd immunity against Covid-19.

To provide the necessary evidence, the Oxford group is working with colleagues at the Universities of Cambridge and Kent to start antibody testing on the general population as soon as possible, using specialised “neutralisation assays which provide reliable readout of protective immunity,” Prof Gupta said. They hope to start testing later this week and obtain preliminary results within a few days.


https://www.ft.com/content/5ff6469a-6dd8-11ea-89df-41bea055720b

Edited by vememah
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