The effect of temperature and humidity on the growth rate of COVID-19

I'm a data scientist. I know nothing about viruses, but I do know mathematics. I have been keenly watching the growth in confirmed diagnosed cases of COVID-19 around the world for the last month. Whilst China has managed to significantly slow the spread of the virus, in many countries around the world, it is continuing to spread at an alarming rate.

The interesting thing is that there are now enough cases in countries around the world that it is possible to do some comparative analysis. I decided to look at the growth rate of COVID-19 cases in each country this morning as, for the first time, the volume of cases in countries around the world means we can start to compare the rate of growth of COVID-19 cases in different countries with some accuracy. The results are in the table above. I only included countries that had at least 30 confirmed cases on 3 March to make the data somewhat reliable.

I started this analysis with no preconceptions, I thought, although one preconception it turns out that I did have is that, on the whole, the UK where I live, is taking COVID-19 quite seriously. On the face of it, the rate of spread of COVID-19 should be slower in the UK than other countries.

However, over from 3 March to 7 March, the growth rate in cases in the UK (for the 16 countries which have enough cases to make the maths significant) has the second worse rate of growth in the world at 4.1x. This is only exceeded by Switzerland that has a growth rate of 4.8x. And surely Switzerland is another country that is taking COVID-19 seriously? On 3 March there were 40 confirmed cases of COVID-19 in the UK and by 7 March there were 164, a 4.1x increase. Although 164 cases might not seem worrying, a 4.1x increase over 4 days means that the number of diagnosed cases of COVID-19 is doubling every 2 days. If the number of cases continues to grow at the current rate, then by 4 April, there will be 3.2 million diagnosed cases in the UK.

I was surprised by the growth rate in the UK and Switzerland. It seems high when many other countries around the world seem to have a much slower growth rate. So I decided to see if I could work out what could be the underlying cause. The first thing I looked at was temperature. Indeed, since COVID-19 has a minimum incubation period of 4-5 days, but can be as long as 14 days, I decided to look and see if there was any correlation between growth rate of confirmed cases and the median temperature over a 7 day period that ended 5 days before the current day. More specifically I looked at the 4 day growth rate between 3 March and 7 March compared to the average mid-point of the daily max and min daily temperature for the period 25 February to 2 March for the most effected city in each country. For example, in London, the average mid-point for temperature for those 7 days was 6.1 degrees Celcius.

The effect of temperature

It turns out that temperature does indeed seem to have a significant impact on the rate of spread of COVID-19. For Zurich, London, Berlin and Paris, major cities of the countries with the highest growth rates, the average median daily temperature was in the range of 5.6 to 6.1 degrees Celcius. For Singapore, Bangkok, Taipei and Hong Kong, the capitals of cities with the lowest growth rates, the average median daily temperature was in the range of 21.3 to 29.8 degrees Celcius. What was the difference in growth rates between those two cohorts? For the first set, the European capitals, the growth in confirmed COVID-19 cases over 4 days was between 3.4x and 4.8x. For the second set, the Asian capitals, the growth rate was between 1.1x and 1.2x. These differences seem large, but their impact is far, far larger. For a country with 100 confirmed cases on 7 March with a growth rate of 1.1x every four days, it means that after 28 days, the total number of cases would be 194 cases, around twice as many. For a country with 100 confirmed cases on 7 March with a growth rate of 4.0x every four days, it means that after 28 days, the total number of cases would be 1.6 million cases. This is shocking, but a simple law of exponentials. Here's the equation: 100*4.0^(28/4) = 1.6 million. Copy and paste that equation into a Google search box if you don't believe me. As there were 164 cases on 7 March in the UK, then, by 4 April, if the current growth rate continues, the number of cases in the UK will reach 3.2 million by my calculation. A 1% death rate (which is conservative in my opinion) would mean 32,000 deaths.

32,000 deaths will of course not happen, as when the number of confirmed cases in the UK breaches 5,000 (by my calculation this will happen on Wednesday 18 March) the UK government will finally realise that the virus is spreading at an unacceptable rate and take action similar to the action which worked in China. They will lock down cities. This will slow the rate of growth and may keep the total infected count to below 100,000 and deaths to around 1,000.

The effect of humidity

In any case, there seems to be a strong correlation between temperature and growth rate. However, what I then found curious was that, although the four European cities all had similar average median temperatures, they still had quite different growth rates for the virus in the range 3.4x to 4.8x.

I decided to search online to see if anyone had done any similar research before and found that there had indeed been various studies on flu over the years that looked at the impact of not only temperature, but also of humidity on the infection rate of flu. The research was quite clear, the lower the humidity, the higher the rate of infection. In general viruses like it cold and dry. The warmer and wetter it gets, the lower the transmission rate of a virus.

So I decided to look at the humidity in all the cities in the analysis over the 7 days too.

Whilst all four European cities had similar average temperatures, they had quite different average humidities. Indeed, Zurich, with the highest growth rate at 4.8x, had the lowest humidity at 71.4% and Paris, with the lowest growth rate of the four cities at 3.4x, had the highest humidity at 86.3%. London, with a growth rate of 4.1x had a humidity of 75.9%.

Note that sometimes the data fits the model too well and, indeed, if you look at the full table, you can see a number of examples where the data does not fit the above model. Some cities with similar temperatures and different humidities have the opposite relationship. For example, Tehran and Tokyo both had an average temperature of around 9.0 and 9.1 degrees Celcius, with Tehran having a humidity of 64.5% and Tokyo having a humidity of 59.3%. In theory Japan should have a higher growth rate of the virus. However, the reality is that Iran had a 4 day growth rate of 3.2x and Japan had a 4 day growth rate of 1.5x. I built a model to predict the growth rate in these countries (I will explain the model more later) and the predictions are that Iran should have a growth rate of 2.0x (based on temperature and humidity) whereas Japan should have a growth rate of 2.1x. So Iran is performing a lot worse than predicted whereas Japan is performing a lot better than predicted. This does not necessarily mean that the predicted effect of temperature and humidity on the growth rate is wrong, it simply means that there are other factors that can have an even bigger effect. One such factor is of course government intervention and collective social action. The impact of this effect has been clearly seen in China, where my model predicts that there should currently be a 1.7x growth rate over 4 days, whereas the actual growth rate is close to 1.0x.

A model to predict 4 day growth rate

I built a model to try and predict the 4 day growth rate based on temperature and humidity. The model I came up with was this:

• 4 day growth rate = (e^(ln(2)/(0.76 x (T + 0.05 H) - 5.4)))^4

Where T is the median daily temperature and H is the humidity on average over a 7 day period ending 5 days before the current date.

The origin of this equation is the "doubling time", the length of time in days it takes for the number of cases to double with my estimated equation for the doubling time being:

• Doubling time = 0.76 x (T + 0.05 H) - 5.4

In short, the higher the temperature or the higher the humidity, the longer the doubling time. The longer the doubling time the lower the 4 day growth rate.

How accurate is this equation? It is probably very inaccurate. Given the low volume of data and the high level of noise in the data points, then, even if it is true that there is a linear relationship between first, temperature and humidity, and second, doubling time, then the parameters are likely a poor guess. However, the linear relationship above is likely to be false too. Moreover, I have done no analysis to work out if the relationship is to do with average median daily temperature and average median daily humidity, or is more to do with maximums or minimums in these metrics? The short answer is that, at this stage, it is likely impossible to know. The equation above is simply an initial stab at what the actual relationship might be.

How can this model help us?

Let's assume that this equation is actually a good model. How can it help us? The following two charts show the predicted impact of temperature on humidity on, first, the 4 day growth rate in cases and second, the number of diagnosed cases expected after 28 days assuming 100 diagnosed cases on day zero.

According to this model, in general, if the median day and night temperature is below 10 degrees Celcius, then the virus will spread fast and end up infecting a very large number of people. Moreover, in general, if the median day and night temperature is above 20 degrees Celcius, then the virus will spread slowly.

Unfortunately there is not enough date from cities with temperatures in between 10 and 20 degrees Celcius to draw any firm conclusions on what the growth rate really is in that range. What we do know is that Madrid had a median day and night temperature of 11.6 degrees over the 7 day period measured, but had a 4 day growth rate of 3.3x. This is still a high growth rate and in fact much higher than my model would predict. It suggests that other factors are having a very negative effect in Spain. Perhaps the Spanish government has been slow to act in giving citizens advice? Perhaps citizens in Spain have not been taking it? Or perhaps my model is simply wrong.

Or perhaps the data for Spain and Australia indicates that humidity may be a much bigger factor than I have modelled. Both these countries had very low humidity levels at 60%. One hypothesis may be that if the humidity falls below 65% the growth rate of the virus will be high even in warm weather. If so then Japan is the anomaly as it had both low temperature (9 degrees Celcius) and low humidity (59%) during the 7 days examined and should be exhibiting a much higher growth rate than the current 1.5x. .

It's also worth pointing out that the average daily high temperature is typically three to five degrees hotter than the average median day and night temperature. In Madrid, the former was 15.7 degrees Celcius and the latter 11.6 degrees Celcius. In other words an average daily high of 15.7 degrees Celcius can still allows the virus to spread rapidly if unchecked at a 4 day growth rate of 3.3x. This is despite the model predicting that the 4 day growth rate here should be only 1.6x.

Nevertheless, if the model above (or one like it) were validated, then it would allow governments to take a much more targeted approach to closing cities, postponing sports events, shutting down public transport, closing schools etc. In short, in my view, if the predicted 4 day growth rate for a specific city is above 1.7x, then the city should be shut down on that day. This would only happen if the median day and night temperature is predicted to be below 12 degrees Celcius (perhaps corresponding to a daily high of 16 degrees Celcius) and if the day is wet, then the city could remain open if the median day and night temperature is 10 degrees Celcius or above.

If we look at the week ahead in London, Thursday and Friday are likely to be particularly bad days for the spread of COVID-19. On these days the median day and nigh temperature are predicted to be 8 degrees and 7 degrees with humidity at 64% and 61%. This corresponds to 4 day growth rates of roughly 2.5x and 3.5x respectively. Perhaps the government should call a long weekend?

Another point is that we do of course expect the weather to get warmer over the next few months. This is of course, good. However, in terms of the overall impact of shutting down a city for a week, the impact on slowing the spread and saving lives will be much greater if done during a cold, dry week, than during a warm wet week. Governments will be tempted to wait until the numbers are much greater before shutting down cities, but this is a mistake. The law of exponential growth means that, if the growth rate was equal in all weeks, then if you shut down a city for a week when the overall numbers are small, then you will have exactly the same overall impact in the long term when compared to shutting down a city for a week when the numbers are large. It is also the case that if you were to shut down a city in a cold week when the 4 day growth rate at its greatest, it will significantly decrease the overall impact whether that week is early or late in the overall timeline.

In case I'm not being clear, it is far better to shut down London in a cold week in March when the overall numbers are small than in a warm week in April when the overall numbers are large. It would save lives.

Looking back at Hubei

During the period of 22 Jan 2020 to 28 Jan 2020, the number of confirmed cases in China, largely in Hubei, increased from 580 to 6,058. This increase was at a constant growth rate of 4.8x every 4 days. After 28 Jan the growth rate started to slow resulting in roughly 80,000 total cases of infection today.

The median day and night temperature for the 7 day period from 15 Jan to 21 Jan was a very low 3 degrees Celcius. I have no data on humidity for that time, but it is typically around 75% in Wuhan in January. In other words, it was the perfect conditions for COVID-19 to spread.

On 23 January 2020, when the number of confirmed cases reached 845, China took action placing a quarantine on Wuhan. By 29 Jan, six days later the growth rate of COVID-19 started to slow.

In the UK we will most likely reach 845 confirmed cases on Thursday or Friday this week.

My recommendation, shut down London from Thursday onwards until the daily mean day and night temperature exceeds 10 degrees Celcius. This might be just a week, it might be longer. Taking action now will save lives.

The impact of quarantining

How much impact will quarantining have? Perhaps the data from China can give us a rough approximation. The government took action when the number of cases was 845 and the result, around 80,000 infections. So the total number of cases ended up at around 100x the number of cases recorded at the point of action. If the UK government takes no action, the total number of UK cases might be 3.2m by 4 April, whereas if the UK government takes action before the total number of recorded cases reaches 1,000, then the total number of cases should peak below 100,000.

In the graph above, until Feb 17 there were only 1,000 cases outside the US and the chart clearly shows that China had COVID-19 under control. The slope of the logarithmic chart shows the growth rate and you can see the growth rate start to fall off from Jan 29 (but was a straight line before this point). By Feb 10 the chart is trending towards a horizontal.

CAVEAT: The analysis I have done took me around twelve hours and would fall a million miles short of the quality required to be submitted to a journal. I have manually copied case, temperature and humidity data into a spreadsheet and may well have made errors, it took a while. I could and should put in a lot more effort and wait for more data in order to make more reliable predictions. Indeed, I hope that much smarter people than me build upon this analysis and come up with much better models and predictions. However, I feel that time is of the essence and forewarned is forearmed. In London, we have a cold, dry week coming soon.

NOTE 1: Thanks to John Lagerling for pointing out this article that says that some Chinese scientists have worked out that 8.72 degrees Celsius is the optimal temperature for the virus to spread (although this may or may not be true):

• Coronavirus highly sensitive high temperatures

Another paper here based on analysis of the spread in different provinces in China suggests that the virus spreads in all temperatures and humidities not just cold, dry environments:

• The role of absolute humidity on transmission rates of the COVID-19 outbreak

This next paper suggests that the virus spreads fastest between 13 and 24 degrees Celcius and 50%-80% humidity. This is counter the idea above that the virus spreads faster in colder weather. Given my analysis had very few data points in this temperature range, their finding could be true:

• Analysis of meteorological conditions and prediction of epidemic trend of 2019-nCoV infection in 2020

NOTE 2: An interesting research paper here from 2010 on a different coronavirus:

• Effects of air temperature and relative humidity on coronavirus survival on surfaces

At 4 degrees C, infectious virus persisted for as long as 28 days, and the lowest level of inactivation occurred at 20% RH. Inactivation was more rapid at 20 degrees C than at 4 degrees C at all humidity levels; the viruses persisted for 5 to 28 days, and the slowest inactivation occurred at low RH. Both viruses were inactivated more rapidly at 40 degrees C than at 20 degrees C. The relationship between inactivation and RH was not monotonic, and there was greater survival or a greater protective effect at low RH (20%) and high RH (80%) than at moderate RH (50%). There was also evidence of an interaction between AT and RH.

At 21-24 Celcius and 65% humidity it seems that for COVID-19 it can survive for 2-3 days on hard surfaces and 3 hours in the air:

• Aerosol and surface stability of HCoV-19 (SARS-CoV-2) compared to SARS-CoV-1

We found that viable virus could be detected in aerosols up to 3 hours post aerosolization, up to 4 hours on copper, up to 24 hours on cardboard and up to 2-3 days on plastic and stainless steel.

At lower temperatures and humidity it seems likely that it survives longer.

As an interesting aside COVID-19 does not like copper (indeed this seems to be true of most bacteria and viruses). So is there a case for hospitals and other public places deploying copper or copper alloy door handles? This paper from 2015 seems to think so using Copper/Zinc alloys at relatively low copper concentrations:

• Human Coronavirus 229E Remains Infectious on Common Touch Surface Materials

Consequently, copper alloy surfaces could be employed in communal areas and at any mass gatherings to help reduce transmission of respiratory viruses from contaminated surfaces and protect the public health.

Some hospitals in France are indeed doing so:

• Copper is great at killing superbugs – so why don’t hospitals use it?

NOTE 3: One commenter suggested that most cases of transmission happens with close contacts indoors. Perhaps cold weather means we stay indoors more and infection from close proximity is more likely. This might explain the impact of outside temperature, but it doesn't explain the impact of outside humidity.

First, I think this report from the WHO is interesting:

• Report of the WHO-China Joint Mission on Coronavirus Disease 2019 (COVID-19)

preliminary studies ongoing in Guangdong estimate the secondary attack rate in households ranges from 3-10%

Between 1% and 5% of contacts were subsequently laboratory confirmed cases of COVID-19, depending on location.

This suggests that if you come into contact with an infected person you have a 1% to 5% chance of being infected and that if you live with an infected person you have a 3% to 10% chance of being infected. It suggests to me that household transmission is NOT the main process of transmission (although if you had 5 people in your household, the chance that one of them becomes infected could be as high as 50%). Indeed, there are now more and more cases where there is no clear tracing back to an infected person. These people were thus infected either by coming into contact with an unknown infected person OR because the virus persists in the environment after the infected person leaves.

Note that the fact that the temperature and humidity play a big part in the rate of transmission does not necessarily mean that the rate of transmission is high due to the virus persisting in the environment. The virus may well survive longer on hard surfaces in cold, dry environments and may well survive longer in the air in cold, dry environments. However, humidity also plays a big part in how the human body protects us from off viruses ... our body's protective systems perform better in humid environments too according to this paper:

• Flu virus' best friend: Low humidity

Here is the author, Akiko Iwasaki, explaining the three factors on YouTube. She recommends purchasing humidifiers and taking long hot showers to improve your body's ability to fight viruses.

Below is a scientific explanation from Professor William Schaffner of how humidity effects transmission of flu in the air. He explains that low humidity makes it easier for the flu virus to stay suspended in the air.

Although here is another paper where researchers found that mucus and other airway secretions expelled during coughs or sneezes protect flu viruses when they're airborne, regardless of humidity levels.

• Flu virus is protected by mucus when airborne, regardless of humidity

The authors' recommendation; homes and offices should employ a combination of increased air exchange rates coupled with filtration or UV irradiation of recirculated air, as well as regular disinfection of high-touch surfaces, such as door knobs, keyboards, phones and desks.

The difference between these two explanations? The second paper only considers how infectious the virus remains in different humidities, it didn't look at how different humidities effect the ability of the virus to stay suspended in the air. Moreover it only looked at how infectious the virus was after one hour at that humidity. The survival time of a virus at all humidities can be much longer than this (5 to 28 days for the coronavirus above).

It's clearly a very complex and multifaceted relationship as to why cold, dry weather increases the growth rate of flu and coronavirus!

But perhaps this is one of the best summarising papers on the subject:

• Mechanistic insights into the effect of humidity on airborne influenza virus survival, transmission and incidence

Case count data collected from here:

• https://www.worldometers.info/coronavirus/#countries
• https://web.archive.org/web/20200308002441/https://www.worldometers.info/coronavirus/

Temperature and humidity data collected from here (Paris example page given):

• https://www.timeanddate.com/weather/france/paris/historic