The Coronavirus Outbreak: Part One – Modeling “Spotting”

Since 2017, in modeling the threat from wildfire on communities in California, the significant new RMS innovation has been in capturing the process of “spotting” (i.e. identifying new outbreaks of fire far from the fire-front). Strong dry winds bring swarms of glowing embers from a raging wildland fire, which can travel long distances. Should these embers settle on shingle roofs, wooden patios or a leaf-filled plastic gutter, a fire will start. Unchecked, the fire will consume a house.

In high-density housing suburbs, wind-driven fire can spread from building to building and consume a whole neighborhood – as happened in the city of Santa Rosa in 2017. And the only way to stop an outbreak is to intervene: to extinguish each ember-ignited fire before it can spread.

Modeling ember ignitions requires sampling the speed and direction of the wind and also anticipating what proportion of fire-starts get extinguished before they can spread. Still it only takes one unchecked fire to burn down the town.

This same process, in modeling “spotting”, is key to anticipating the spread of the new coronavirus into western Europe and North America.  

To start with, managing the risk brought by each newly-identified infected individual will be straightforward. Transmission can be extinguished by moving the patient into isolation and tracing and quarantining all their recent contacts. This process is nonetheless laborious and expensive. The ability to trace and isolate contacts declines as the number of new cases increases. Just as the firemen in Santa Rosa in October 2017 became overwhelmed by the ferocity of the ember blizzard, too much new contagion will crash the system.

Contact tracing, like firefighting, is itself quite a dangerous activity, likely to bring you into contact with those who are infectious. One or two new infections each day can be manageable. Twenty or fifty and it is out of control.  

How would we parametrize our model of viral spotting? Government ministers and health officials make reassuring noises about the degree to which the situation is under control, but is this based on overconfident assumptions?

The first wave of viral spotting is coming from China. Cutting off air travel with China, for a while at least, is like calming the wind. Countries that have cut off all domestic carrier flights to China include Canada, Egypt, Finland, Germany, Indonesia, Israel, Italy, Kenya, Morocco, Oman, Rwanda, Spain, Turkey, the U.K. and Vietnam. Other countries including India, New Zealand, Netherlands, Pakistan, Singapore, South Korea and the U.S. have maintained some flights.

Yet things will be more difficult should there be a second tier of countries in which the virus is now rampant and unchecked. To start with, these could be countries in the vicinity of China, in particular those with weaker healthcare systems. On January 28, after identifying 19 cases in the country, Thailand’s Health Minister stated that “… we are not able to stop the spread…” of coronavirus in the country. On February 4, it was announced a woman from South Korea had caught the virus while in Thailand. Singapore has a strong healthcare system but also receives large numbers of visitors from China. Vietnam has numerous connections with China as does North Korea.

Countries in Africa and South America also have connections back to China and a very limited ability to manage an outbreak. Suspected cases have already been identified in up to eight countries in Africa and South America including Ecuador and Equatorial Guinea. (Many of these countries do not even have the capacity to test for the specific virus.)  

The Months Ahead

Roll the calendar forward to late April and May. The pandemic may be rapidly expanding in some poorer countries. So, taking the U.K. as an example, do you end flights to the U.K. from Bangkok, Singapore, Delhi, or a wide range of cities in Africa and South America?

Are we going to send planes to rescue British citizens from Thailand, Vietnam, India if these countries are swamped with cases?    

Less likely, the virus could also grow out of control in a European country. On the French flight from Wuhan on February 3, thirty-five passengers were said to be showing symptoms. Many foreign nationals were then put on flights back to their home country rather than placed in quarantine. If the virus is spreading out of control in France, how would the U.K. monitor arrivals through the Channel Tunnel or check migrants arriving on a boat?

What happens in the U.K. over the next two months will come down to how fresh viral infections are managed, and not only in the U.K. Will the response to viral spotting be enough to keep the country free of the pandemic, or will the system become overwhelmed as the worldwide incidence rises?

The movement of the virus to other countries would mean we have new sources of the viral embers and it may be harder to identify them as “burning embers” before they land. In the York University student infection healthcare officials came up with some simple rules for tracking contacts (such as that “contact” had to last more than fifteen minutes), but clearly the virus could pass in a minute. Tracing contacts may be easy when it comes to identifying your housemates, but more challenging when finding who was standing next to you on the train. Already, in more than one instance outside China, bus drivers picked up the infection from their passengers.

If you are an optimist, you can hope the viral infection could weaken as it propagates. Or that the rate of infection seen in China is not replicated outside that country. Or you can hope that a novel form of treatment is identified, for those who are lucky enough to find a hospital bed. In modeling the potential pandemic we will also need to estimate when does the vaccine arrive? How rapidly can production be scaled? Who gets it first? Or, as with SARS, will the vaccine arrive too late?

The viral mega-tsunami is rapidly growing, but so far, outside China, people seem to be strangely unconcerned and unprepared.

We still don’t know the mortality rate. If it takes an average of a week to pass from first symptoms to death, then should we compare today’s cumulative death rate with the number of cases identified a week ago? That would give a death rate as high as ten percent. However, it is suspected that many milder cases are not being reported, which would swing the percentage to lower levels (even down to the “two percent” that is widely quoted), as would shorter times between disease identification and death.

We do know that the cumulative death toll is currently doubling every four days. At this same exponential increase, by early March it will reach 50,000.

If you want to know the probability I would assign to this outbreak growing out of control, across the world, then you should know that on January 22, I bought a supply of surgical masks.