Why the Western approach to COVID-19 pandemic may be dangerous. Mitigation and Suppression effects seen on the models.

Combined mitigation and suppression effects on number of infected

Everyone seems to be talking about pandemics now a days, and in all truth the reason is simple life will never come back to what it was for many reasons. The first one is that the world is in a big corner, either we all get immune to the virus or we live in social exclusion until we get immune to the virus. There is a great probability that if we take option two world population will have to decrease or we die either by being killed by some one or of hunger. There seems to be no way out from getting somehow immune to the virus.

Going back to a previous post; models help us understand what will happen if we choose to follow specific scenarios. Contention, mitigation and suppression are the pillar of any pandemic reponse. The contention response is to identify and neutralise all the virus possible whereabouts and is possible and effective at the very first stages of the outbreak. The mitigation response comes into play when the virus whereabouts cannot be determined for it is everywhere and a more broad spectrum of isolation of communities are required to contain the outbreak expansion. The suppression response is defined by an active search of any affected individuals and locations independent of the virus whereabouts. I will focus on the approach of the SIR model defined in: https://scipython.com/book/chapter-8-scipy/additional-examples/the-sir-epidemic-model/

I will not go into many details just cite the model equations that describe the SIR model. And go directly to what the reader wants to know. Where are the variables in the model? What variables can relate to mitigation? What variables relate to suppression? What happens to the simulated outbreak response on any of these two cases?

“The differential equations describing this model were first derived by Kermack and McKendrick [Proc. R. Soc. A, 115, 772 (1927)]:” see link above for original publication.

  • S(t) are those susceptible but not yet infected with the disease;
  • I(t) is the number of infectious individuals;
  • R(t) are those individuals who have recovered from the disease and now have immunity to it;
  • β is the effective contact rate of the disease;
  • γ is the mean recovery rate where 1/γ is the mean period of time during which an infected individual can pass it on.

The differential equations can be seen below.

SIR model differential equations
SIR model differential equations

The models effective variables are population number N, contact rate β, recovery rate γ and S, I and R initial conditions. Mitigation effects are mostly related to β for the number of people we can influenced is reduced if we stay at home. On the other hand suppressive measures are more related to γ, for we cannot change a virus recovery time without medicine we can only search and isolate contaminated people. Suppressive measures mean we measure everyone and segregate as many times possible until we find all infected. Each time we find a contaminated person before the recovery date we shorten the virus propagation time.

Sending everyone home is a mitigation effect not a suppressive effect because if a contaminated person goes shopping for food there will always be a chance/opportunity to propagate directly and indirectly the infection through out the viral infectious time.

Three experiments were performed to evaluate the efficacy of these approaches:

    • Mitigation effect on number of infected β[0.15, 0.2, 0.5] and γ = 14;
Mitigation effects on number of infected
Mitigation effects on number of infected
    • Suppression effect on number of infected γ[7, 14, 21] and β = 0.2;
Supression effects on number of infected
Supression effects on number of infected
    • Combined effect on number off infected β=0.15 & γ=14, β=0.2 & γ=7 and β=0.15 & γ=7.
Combined mitigation and suppression effects on number of infected
Combined mitigation and suppression effects on number of infected

Every time we catch an infected subject we reduce the 14 day propagation probability to 1 day if we are lucky and catch really early. Even if we catch the subject on his 7th day of propagation we dramatically impact the pandemic evolution.

So my recommendation is test, test, test, test. The impact is strong!

Hopefully with this simple mathematical demonstration it makes clear that only a combined approach will yield effective and fast results, considering that a vaccine will take some time to be developed. However this is not a solution. The world will have to live in containment until we get some sort of immunity to the infection.

I am completely aware that from theory to practice there is a long and hard way. However I think everyone should be prepared to do what’s necessary to avoid a complete social collapse. On a pandemic scenario we cannot have everyone for them selves because our economic model is a shared model. We base our economy on collective consumption of food, cars, vacations, houses, gadgets, and the list goes on…

Going back to my first post, it makes me be afraid of the Western world approach of Mitigation with not so organised suppression. Western results may not be what everyone expects because this virus can contaminate an individual, spread and not give any symptoms. It seems for this kind of infection suppressive measures combined with mitigation are the correct way to proceed.

Some remarks; although for simplicity I considered staying at home a mitigation effect and active testing a suppressive effect, in reality things are more complicated. If we manage to make an individual stay the 14 days at home with no transmission possibility, all two factors are affected β and γ. In reality population continues to circulate and only time will show, how much we can affect these variables.

My final words:

  • We need urgently one central pandemic headquarters – Global;
  • We need urgently region epidemic headquarters – Europe – Asia – Africa – America;
  • We need to distribute help to the countries that need most;
  • We need to distribute fast/updated best practices to everyone;
  • We need to find a way to immunise population and have the courage to do it. To wait a year is not an option.
  • We need to create virus free zones where we can have more relaxed containment measures to let part of the economy survive.

Novel coronavirus (COVID-19) a World Pandemic where we are now.

SIR model

I have been following with a bit of apprehension the COVID-19 pandemic evolution around the world, from Asia to pretty much all over the world. Human kind has lived and until now survived many epidemics and pandemics, but this virus seems to have taken everyone by surprise, where even many important nation representatives showed no interest in dealing with the pandemic calling it, a simple flue virus.

The pandemic, initiated in China Hubei Province in Wuhan. After a slow start by the Chinese governement to grasp the scale of the epidemic (at that time) it took tough measures, really going to extremes to contain the virus. It seems that their effort showed results and at this point China controlled the Pandemic in their territory but unfortunately has not solved the problem. Although the number of cases have reduced to zero, or almost there, it is sustained at high control and pressure measures. I can’t see any tourist wait 14 days quarantine to discover China, maybe only a few could afford it. Markets, shops, transportations services that serve millions will have to be limited.

Asian countries took the Pandemic seriously and prepared for the worst, closing borders, testing, isolating contaminated people and preventively reducing human circulation.

Europe on the other hand seems to be the new Pandemic center and Italy, it’s most affected country, having high number of deaths and many new infected cases every day. Throughout all Europe the pandemic seems to be growing without stop. It seems Europe took more time to implement hard measures and seems to be on the defensive side to reduce the number of new cases to avoid overcrowding their health care systems.

In the USA after a dangerous denial period the disease seems to be taking over and forcing many states to take hard measures, which in turn forced their president to declare national emergency. Interesting the UK and Brasil followed the American denial, however the growing numbers of infected people and deaths slowly but surely is changing state representatives opinion, that in turn make their presidents change stance.

In Africa we are starting to see a slow rise in cases, however numbers are expected to explode, in the comming weeks/days, for they do not have the capability that most developed countries have to deal with this pandemic.

This Pandemic, like any other can be dealt with mitigation actions like prophylactic containment and/or by suppression actions, which mainly consists of mass individual testing. The Asian countries and the Western countries are using different tactics to deal with the Pandemic. Asian countries use extreme mitigation actions combined with suppression actions which until now have proven to be effective. Interestingly the Western countries seem to be on the defensive side with mostly mitigation actions, with however not so effective results. A good explanation about this can be seen in the following link: https://www.theatlantic.com/ideas/archive/2020/03/how-we-beat-coronavirus/608389/

Interestingly Italy tried with very good results the usage of suppression actions on the pandemic but on a small scale. The difficulty to implement these actions on large cities with generalised infections is that it requires a great deal of resources and organisation. A good report on this subject can be seen here: https://www.ft.com/content/0dba7ea8-6713-11ea-800d-da70cff6e4d3

Certainly East and West have used models to predict the pandemic evolution, scientists, politics and the general community certainly got shocked when they noticed that doing nothing could yield total chaos. Models predict an insane amount of infected people at the peek of the pandemic.

Models help us understand and predict the behaviour of Pandemics. A good reference to understand what models exist and their boundary conditions can be seen in this article: https://chengjunwang.com/post/en/2013-03-14-learn-basic-epidemic-models-with-python/

The SIR model (S – Susceptible, I – Infected, R- Recovered) can help us understand the severity of our current world situation. For example for a 1 million population, 14 day mean recovery (time during which an infected individual can pass it on) and 0.2 value factor that compensates the rate at which an individual can come in contact with others, gives us a good prediction of what to expected of any epidemic response.

In this demonstration example case, almost all of the population gets infected and we get an infection peek of more than 20% of the population. No health care system can deal with such a wave.

I will end this post with a few questions that are in my mind so far:

    • Will the Western approach of low suppression (reactive to symptomatic patients) and high mitigation be enough?
    • Are the models used by scientists taking into account the fact that infected people don’t know they are infected and don’t present symptoms?
    • Even if we control the outbreak, how will the economy survive if most of us fear a second wave due to lack of immunity towards the virus?
    • How long can the world live in social containment?
SIR model
Pandemic SIR model (see https://scipython.com/book/chapter-8-scipy/additional-examples/the-sir-epidemic-model/