Italian Version of this article: https://www.linkedin.com/pulse/modellando-levoluzione-di-covid-19-italia-ettore-mariotti

Follow up: https://www.linkedin.com/pulse/covid-19-europe-who-next-ettore-mariotti/

As of the 5th of March, 77 countries have reported the presence of novel coronavirus (CoVID-19) on their territories, raising the global number of people infected to 93'090. Italy stands now as the third country as regards the number of infected people, with 2'502 confirmed cases, and second only to China in relation to the number of deaths (80).

Since the beginning of the epidemics, lots of CoVID-19 spreading models have been reported, but due to the viral diffusion genesis, most of them have been more concerned about dealing with Chinese data. Here, we attempt to model the evolution of the CoVID-19 outbreak in Italy, as well as to draw possible scenarios based on the degree of containment policies.

How is it possible to model a phenomenon so complex that depends on biology, social interactions, economic interests and politics (just for naming a few)?

By making some assumptions.

In epidemics there exists a class of models that historically were proven to be quite a reasonable approximation of the future: SIR model.

The idea is first of all to consider an "isolated island" where people are constrained to stay, no one can leave. Each person can be in one of only three states: "Susceptible", "Infected" and "Recovered" (Here the acronym S-I-R). With some probability people that never had the disease (S) can become ill and infective (I) for a certain period before recovering (R). Recovered individuals are assumed to have the special property of never getting infected again (so we will put deaths in this category too). In the case of CoVID-19 it is appropriate to extend the model with an additional state "Exposed": people that have the virus but are not infective yet.





The parameters of the model (and thus, its evolution) depend on two things:

1) Details about the Virus dynamics (not too hard to estimate)

2) Details about human mobility and interaction with other humans (much more complex to infer)

With this set of assumptions we are able to compress the richness of the interactions between the virus and our interconnected world and social network with a single number: R0. This quantity represents actually quite a simple concept: "given that I am ill, how many people will I infect? (on average)". Let's pretend for example that today person A is ill and that our system+virus is described with an R0 of 2. This would mean that tomorrow A will have infected 2 people. Those 2 people the next day would have infected 4 people, the next day each of the 4 newly infected people would have infected 2 other persons (thus 4*2=8) and so on. This reveal us the multiplicative nature of contagions (as opposed to an additive one).

But how all of this fit with CoVID-19? Data is scarce and thus a solid estimate of R0 is difficult to make, but by observing historical records we can get an idea of what this quantity could be by measuring how steep is the growth of newly infected cases.

But hey, why two R0s? This is because society can lower its connectivity as a protection mechanism for reducing the diffusion of the disease. And for example by keeping schools closed, sport events without public, gyms closed, postponing concerts and in general reducing events of high social interactions we lower the possibility of contagion between individuals. All of this translates to a lowering of the R0 and its effect can be seen in the plot above. The orange line shows the progression of the disease with its "natural" pace, while the blue curve shows how the aggressiveness of growth is at least partially mitigated by these norms (it takes a while for containment policies to show their impact on data).

Is this enough? Are we ok with an R0=1.7?

It turns out that the construction of the SIR model (and its extension SEIR), allows us to derive an important result: the disease spreads to all the community if it has an R0>1, the disease quickly disappear if it has an R0<1.

So why should we care about lowering the R0 if it still remains above 1?

Even though the theory predicts that after a long time most of the "island" will be taken over by the virus (with R0>1), it is of great importance in assessing how impulsive this process will be. In particular and most importantly a lower R0 helps in not having everybody sick at the same time. Let's keep in mind that our healthcare system has finite resources (i.e. a more or less fixed number of intensive care unit beds) and could be not able to guarantee appropriate care in the face of an overwhelming demand.

But enough with the theory, what does the simulation say?

First of all: this is a "What if" scenario projection. In particular these plots answer the question "What would happen if we let things evolve as they are?". This pictures should help us realise several things:

1) R0<1 evolves naturally and relatively quickly toward a disease-free world

2) It is always of value to lower R0, as it keeps the peak lower and more into the future (a lower burden on the healthcare system)

3) We should act, and should act quickly. We should not be fooled in thinking that every day we have "x people more than yesterday". We should begin to see the bigger picture by realising that we have "x times more people than yesterday".

If we look carefully at the estimated number of people that will need hospitalisation (computed as ~9% of the infected, as reported by salute.gov.it) with respect to the capacity of the SSN (Sistema Sanitario Nazionale) the concern becomes even clearer

It is reasonable to expect that the governments will impose more strict constraints on mobility in the tentative to reduce the R0. The practical measures that there will need to be taken are a complicated trade-off between the economic damages that containment policies will do (as a lack of productivity) and the economic damages if no containment at all will be made (Overloaded healthcare system, old and weak people in serious danger). It is nevertheless important to remember that we are not dealing just with economic repercussions, but we also talking about life and human suffering.

So in conclusion, by quoting John Oliver: "How much should we worry?"

and the answer is: "Probably a bit."

Of course panic does not serve any good, but a conscious attention to the problem can help us to understand the problem and act skillfully. We should find the sweet spot between running naked in the streets calling for the Apocalypse and dismissing this event as a "banale influenza" and living as nothing bad will ever happen. The containment of the epidemics is a responsibility of both government(s) and society, and we are the society.





This article and the work presented here is the product of an interdisciplinary collaboration between me (Ettore Mariotti), Nicola Lissandrini, Marco Ceccato, Matteo Zanovello and Tommaso Ceccato