How will the COVID-19 (coronavirus) epidemic end?

When will the COVID-19 / coronavirus epidemic end? How many people will die from it? How many people will get an infection? How much should you worry about it? This video hopefully can give you a sense of what to expect via a simple mathematical model. It is a standard one with reasonable accuracy, called the SIR model, which illustrates exponential growth / decay depending on the ratio between two constants, called the basic reproduction ratio / number (i.e. R0). The prediction from the model is not that optimistic...

We are still in the exponential growth stage, but eventually it has to be a logistic curve, and the video discusses where the plateau will be, and the time scale at which the plateau will be achieved.

The measures that can be taken to reduce the number of infected individuals, as in the last part of the video, should give enough context to show how seemingly insignificant local measures can have a huge impact, and ultimately persuading the public to stay on alert and take part in those measures described.

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[mathemaniac]

This is not made with the intention to elicit unnecessary fear. But we do need to be on high alert.

1st note: Predicting epidemics is always difficult and this is only a simplified model which does not take many other important factors into account, like weather; and we implicitly assumed that everyone has an equal chance of getting an infection, which is not true.

But don't let the inaccuracies of this simple model overshadow the supposed conclusion at the end of the video, which is valid in every epidemic: these common-sense local measures can help massively and actually determine the global scene of epidemics. The so-called "flattening the curve" does not only help the medical system, but also actually decreases the number of new cases if we can limit beta to even be just very slightly below gamma.

2nd note: for the very high plateau of billions, the vast majority of cases is still recovered, but even with just a tiny proportion of death (like a death rate of 0.1% like seasonal flu) still puts the number of deaths in millions, let alone the current estimate of 3.4% by WHO, so this is still a serious concern.

3rd note: there is another way to increase gamma very unethically: to make the disease even more deadly. This idea is not only unacceptable, but also very cruel. But the reason why it works is that fewer people can actually spread the disease. This is also why MERS (with a fatality rate of 36%, i.e. gamma is at least 0.36) only gets very few cases (under 2500 cases). Actually, the higher the fatality rate, the fewer cases there would be, because in addition to being actually less likely to spread, but also that people are on higher alert. The epidemics which kill a significant number of people are usually those with reasonably low fatality rate, a counterintuitive fact that not enough people understand.

4th note: incubation period. The fact that people can spread diseases symptomless can make the data underreported, but even without considering incubation period, the prediction of this simple model is already pretty disastrous.

Let's get our hands together (actually no, but figuratively) and we can fight coronavirus!

[peterjohnson]

As a fellow mathematician ( doing his master's) you are one of the few on the platform here who actually has talent in explaining mathematics. Keep up the work.

[mathemaniac]

Sorry for the interruption in the video series for group theory. I will get back to that video series after this video :)

[trinitytwo]

This is assuming there is no mutation in the virus, and we have immunity. The second wave of the 1918 flu was the most virulant.

[RefluxCitadelRevelations]

Hello from 2021.
Sorry past humans...

[bosoerjadi]

Aren't the data warped? The daily number of newly confirmed cases, especially the first few weeks, are probably rather a reflection of current global testing capacity, than of actual rate of infection.
In the extreme and ridiculous: if nobody gets tested anymore for infection, beta drops down to naught, gamma increases exponentially as all previous confirmed cases either recover or die. According to the numbers we then would have "won the war", while reality insists to differ.
I believe it makes more sense to focus on the course of the pandemic in certain wealthy countries first. Where testing capacity is more abundant and (sooner rather than later) not a limiting factor anymore in establishing infection. Before including the entire world. Consistent quality of data over the entire time frame is at the foundation of any analysis, after all.

[mathandsciencereboot]

I wish more people will watch this so that more people will understand the nature of this pandemic. It is highly politicized.

[bisbeejim]

I am a math student. My teacher makes the mathispower4u videos. On the side I study psychology and computer science. With the math I know (math less complex than what you are using) I calculated the same results. I went a step further to calculate the psychology of a person receiving bad news. That is the psychology of 1) denial, 2) aggression, 3) bargaining, and 4) acceptance. Four logistics curves are represented with a 21 day point between their inflection points. The graphs predicts the psychology of bad news behavior with X as time and Y as number of people acting out denial, aggression, bargaining and acceptance. It predicts the aggression wave will be present in earnest in the United States on April 1st, 2020.

[chrisnielsen]

Thanks for uploading. With the logistic growth function the inflection point in Denmark is about 40-50 days. But reliable data is of course not easily obtained. And this is only the first wave of infection. Keep up the good work. Subscribed.

[StevenTorrey]

I didn't realize "recovery" also meant "death" as well as "recovery".

[carsandguitars]

Excellent video.The I part the SIR model is very hard to get exact at any moment unless every single person on the planet is tested.When you look at the new US cases they growth dramatically every day, one big reason for that is the testing there is really being ramped now.So there could be so many people infected and are showing minor symptoms that aren't being reported.

[quinndtxd]

is there somewhere I can get this information but more up to date? (I havent looked yet though, there might be more on this channel :P )

[StevenTorrey]

As of March 24, 2020--the number of infected people is 414, 277 with 18, 557 deaths. This video used the date of March 11, and here it is March 24, so something like the 20 days of infections; at this rate we will be well into 1.87 billion infections within just a few months. China saw a leveling off of infections after a little more than 12 weeks; Italy seems to be showing no leveling off after about 8 weeks.

[coll]

Good Job but I would still use the logistic model. Given that many recovered patients still get reinfected, you might have to recycle that number back into S again which will give a continuous iteration in the SIR model. This gives the logistic model an edge.

[mili]

Thank you for an excellent video!! I’m so happy to have found your channel. I hope to watch more of your more advanced videos soon

[dougaltolan]

Except the SIR model is woefully inadequate. Ehat you need is the SIRGPIbD model: Susceptible, Infected, Recovered, Government, People, Idiots, bloody-minded Determination

[oneminutethoughts]

What type of network architecture you used.? a fully connected one I suppose. Actual rates are lower than those measurements when you use a different architecture, something more close to the realistic scenario.

[thejils]

This model might have been applicable to COVID-19 kinetics if it weren't for the fact that there are unknown numbers of asymptomatic carriers in the whole world population at large at any given time. To deal with this uncertainty, which is a direct consequence of incomplete COVID-19 testing throughout the world, just assume that EVERYONE on the planet has the virus at time=0, when patient zero presented with symptoms. Now, all we care about from that time moving forward is the rate of bonefide, clinician-diagnosed, test-positive, COVID-19 illness in the entire world population. This will also take into consideration people that had the illness, recovered, and then became ill again from presumed second virus exposure because at this stage of our knowledge about this virus, we don't know about the effectiveness of herd immunity in preventing reinfective illness (presumably, eventually our COVID-19 diagnostic testing will be able to ascertain old vs. new vs. no COVID-19 exposure, which will help give us a handle on re-infectivity rate). Now, currently there may be a reportability problem. In diseases gone by, when number of cases of a particular disease was reported, it was meant to imply SYMPTOMATIC disease. Not so so with COVID-19: when we see number of COVID-19 cases, it is reflective of BOTH symptomatic and asymptomatic cases. Now do you see why assuming every human on earth has the virus is so important: because now we can determine an actual rate of SYMPTOMATIC disease in the human population at large. From this value, at any given time we can report and then find rates of recovery, rate of mortality (and eventually morbidity), and rate of re-infection.

[itsnony]

This model needs adjusting. South-korea is reporting people showing up positive again after recovery, meaning the R in this SIR-model is wrong.

[syamkriz]

There seems to be some problem with graph. It is now showing a straight line