After some days of model development and calibration it is now time to see if our work can predict the outbreak in Portugal.
Using yesterday’s data of the Portuguese outbreak we can see if the model can keep up with the outbreak evolution.
The new infections per day report:
The results show that there is a diference from the predicted infections compared to the actual measured infections.
From the graph we can see that the model can still predict the evolution up to now.
From the close up image we can see a horizontal offset. We will need more time to evaluate if this will continue on probably due to mitigation and suppression activities or if it is simply a counting issue.
The way we affect our model may change from a simple decay function to something really messy to represent reality.
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.
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;
Suppression effect on number of infected γ[7, 14, 21] and β = 0.2;
Combined effect on number off infected β=0.15 & γ=14, β=0.2 & γ=7 and β=0.15 & γ=7.
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.