Thank you for this very nice introduction and I thank you but I also thank the University

of Erlangen for letting me present these very, very, very recent results.

Next please Marius.

I organized my presentation in three parts.

First to explain to myself and also to the audience of course what is a multi-scale vision

in a globally connected world.

Then I will outline the modeling strategy and finally I'll reach the most important

problem now that they have to show how the multi-scale vision gives to mathematical models

and description of possible scenarios of the pandemic.

Next please.

I have to say first, well actually it was already said by Enrique that these results

are coming from a very recent paper.

What I would like to outline is that this paper is effectively interdisciplinary because

in addition to some applied mathematicians, myself and few others, we have a virologist,

I mean Bingham and Twarock, economist Giovanni Dosi and Marica Virgilito and one immunologist

Guido Forni who is an old friend of mine who introduced me to the complexity of the system

around 25 years ago.

One of the motivations in addition to the scientific and to the overall situation has

been also an initiative coordinated by the Royal Society in the UK.

It was a voluntary project and we voluntarily joined the team of the In-host Modeling and

actually this is the topic I'm going to talk about.

Next please.

What to say about what is COVID?

Well, COVID is related to something that has been induced by SARS-CoV-2 and then these

mutations generated what we know as COVID-19 which generated the subsequent pandemic.

Several governments mentioned the Black Swan as an event of our society.

Actually COVID-19 has only partially the properties of a Black Swan because it is true that it

has modified and a huge impact on our life and modified our life.

On the other hand, the virus problem was not so not predictable.

Bill Gates made a conference on this matter and definitely something could have been foreseen.

Not exactly COVID-19 but virus pandemic is something we should care about as we are caring

about heating and other possible tragedies for our world.

What I would like to stress about the very brief description which is given in the slides,

please go ahead Marius, in this description what is important is to mention the competition

with the immune system.

When the virus manages to overcome the barrier of the mechanism in the mucous secreted by

the goblet cells, then there are rapid danger signals which activate the immune system leaving

for what we know as the innate immunity.

This is the same level all of us have and if these signals are registered then the immune

system activates and learns the presence and fight against.

Actually coronaviruses are in general successful to suppress some of the defense mechanism

but luckily not all of them.

Therefore, it is not like cancer cells which can hide all mechanisms, mute all mechanisms

but there is a problem because the virus proliferates, the immune system activates but there is a

competition.

So on one way, medicine should reduce the proliferative ability of the virus and on

the other hand the immune system should be active.

Going to the modeling, please next Marius, going to the modeling, some general ideas,

very general ideas.

First of all, I feel that we should go far beyond the deterministic population dynamics.