COVID-19 pandemic growth in Portuguese territory

All over the world we start to get richer datasets of the pandemic evolution in each country. Portugal is a small country on the western extremity of Europe next to Spain. Let us examine the numbers.

The Corona Vilan
The Corona Vilan

The results are based on the python code shared by: https://scipython.com/book/chapter-8-scipy/additional-examples/the-sir-epidemic-model/

With some modifications to take into account transmission rate and mean recovery time variation through time.

I also have to share some good resources from Stanford University and the Imperial College of London: 

On a previous post I introduced the equations:

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

 

On my model Instead of having a constant β and γ we have time dependent functions B and G based on the decay function:

SIR model adapted differential equations
SIR model adapted differential equations

 

Measured data was gather from HDX compiled by Johns Hopkins University Center for Systems Science and Engineering (JHU CCSE).

Here we can see the daily infection cases in Portugal which is following an exponential.

New infections in Portugal
New infections in Portugal

 

And also observe the current pandemic infection count in Portugal:

Measured data
Measured data

 

The resulting B and G estimation curves can be seen bellow:

Contact rate Beta
Contact rate Beta

 

Gama recovery time evolution
Gama recovery time evolution

 

The model seems to fit well to the measured data at least for now.

Close up Model vs Measured prediction
Close up Model vs Measured prediction

 

Zooming out we get:

Model vs Measured prediction
Model vs Measured prediction

 

And yet another view:

Close up 2 Model vs Measured prediction
Close up 2 Model vs Measured prediction

 

The model predicts the following:

COVID-19 model prediction results
COVID-19 model prediction results

 

If the prediction is correct we should expect to have at the peek of the crises 331388 reported infection cases. Hopefully less than 2% of these will require a ventilator (6627 ventilators). My concern is that the usage time of ventilators can be greater than the 14 days estimated.

The ability to compensate the model curve based on time dependent factors is efficient to adapt the curve to experimental results.

We can see that the mitigation and suppressive actions have payed off giving a softer but longer epidemic curve.

As we get new measured data, the model precision increases for we refit and generate a new model. If the mitigation actions continue it is expected that the peek value continues to decrease, however time will increase.

My final remarks: there will be no guaranty we can lift the heavy restrictions to contain the spread. Humanity will live in fear and alert until we find a vaccine or get herd immunity.