COVID-19 from a Network Science perspective

Starting on December 31st 2019, in the Chinese city of Wuhan, an outbreak of a novel coronavirus (COVID-19) made its appearance and in less than two months it became a global health crisis. At the time of writing this article, 181,562 cases have been confirmed worldwide, out of which 7,138 deaths were caused by the virus. The World Health Organization (WHO) has already described the outbreak as a pandemic.

At the moment, the virus seems to be unstoppable because of its rapid spread and the fact that we still haven’t found a cure or vaccine for it. The exponential growth of infected people in several countries has raised many concerns and requires strict measures to be taken in order to slow the spread of Covid-19 outbreak.

Let’s see the math behind that rapid spread…

Branching Process

Epidemics act in a branching process.

First wave

Assume one infected person meeting people and contaminating them with probability p. That concludes in having the first k people to become infected.

Second wave

As the k infected people go on infecting others, we get the second k*k to become infected.

Subsequent waves

Each person in the current wave meet k new people, passing the disease to each independently with probability p. So the n-th wave will get k^n more people infected.

That’s how we get to what we call exponential growth.

As for the probability of contagion, it appears that due to the virus characteristics, it is contagious enough to worry about. And high contagion probability means that the infection spreads widely.

Node Infection Model

Now let’s take a look at the node states of an epidemic.. And by nodes we actually refer to humans.

Node state: one of possible conditions a legitimate node lies in.

The possible states of a node are the following:

  • Susceptible, S(t): prone to receive a disease
  • Infected, I(t): node that already received a disease
  • Removed, R(t): infected and totally recovered
  • Dead, D(t): removed from a network

Given the fact that there is no cure or vaccination yet to lead infected to full recovery or immunity and also, that it is not unlikely for patients who have recovered to receive the disease again (or at least, that scenario hasn’t been denied yet), we have the following model:

SISD

Although most infected people return to susceptible state, there are unfortunately deaths, and that’s why science desperately needs to get us to the following model:

SISRD

The SISRD model is different from SISD because of a vaccination that could get us from susceptible state to full recovery without even being infected and a cure, that would lead infected people to fully recovered. Of course, whoever doesn’t receive treatment or vaccination would be led again to S or D state.

Keep calm and stick to some rules

Until we get to SISRD, let’s see what measures could be taken to make SISD viable and most importantly, minimize D node states!

Rule 1: Social Distancing

The most important rule is the one of social distancing. Remember the branching process explained before? Since Covid-19 is quite contagious, the more people an infected person meets, the more “branches” are created. Thus, infected people should stay home until they get to state S again and avoid meeting other people. Seems legit. But what about the non infected? Should they stick to the rule of social distancing, too?

The answer is yes, because that way they’re fighting the probability of contagion and stop the branching process of the epidemic.

What we need to do, in order to help slowering the spreading of the disease and help more people get back to state S and avoid state D, is focus on S and I states as if they’re the same. Same rules for S and I, both staying home, so that they are not in the “network” of the epidemic anymore.

Getting quarantined is not so scary as it sounds, nowadays. There are several stuff to do while staying home, like reading books, working out, watching movies.. And of course, if the nature of your job allows it, work remotely 🙂 Needless to say, there are so many alternatives you can use for a groupware software: file sharing, collaborating on documents, video conferencing etc. If you’re not fond of the Big 5, take a look at what we’re doing in LaceWing Tech 😉

Rule 2: Good Hygiene

Sooner or later, you may need to go out (buy something, work, etc).. In this case make sure you keep an antiseptic gel close and wash your hands often and thoroughly.

Rule 3: Keep calm

If people are sufficiently worried, then there’s a lot less to worry about. But when no one is worried, that’s when you should worry. So spread the word, keep calm, stick to the rules and things are going to get back to normal soon.

The only thing to fear is the lack of fear itself.