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On the impact of Contact Tracing for virus containment

UPDATE SUMMER 2021:

In Italy automated contact tracing never had success. The app was downloaded by 1/6 of the population, making it fail to help reducing the contagion, as predicted below. Indeed, after the first big lockdown, the virus spread was so reduced that a second wave was not taken seriously. As we have seen, a second wave was produced at the end of the summer and was even more dramatic (during summer the virus seeded in the whole peninsula, while the first lockdown helped preventing it from reaching the south of Italy). Its rise was slower than in my models because individual protections and distancing norms were introduced by the governement and reduced the virus R0 to a lower number.


In my last post, I have tried to fairly weight the role of information and communication technology (ICT) in the spread of the Covid-19, highlighting what is controversial with recent attempts of exploiting deep learning for sensitive diagnosis tasks. Here, on the other hand, I will show how ICT can help us fight the coronavirus on another ground: contact tracing.

What is contact tracing? If you need a quick introduction watch this comic from Nick Case: [English | Italian]

Several governments are now discussing the introduction of a so-called contact tracing App to reduce the spread of the Covid-19 disease, following the footsteps of a few early adopter states. The concept is simple: use a smartphone App to keep record of contacts with people met in the last days, so that they can be alarmed if you happen to be positive to the virus.

Suggested strategies can differ and none is yet winning. However, the use of GPS seems to be currently avoided by most governments, in favor of protocols based on the transmission and book-keeping of Bluetooth hash codes. The latter, combined with distributed strategies, secure communication protocols and open-source audit of the code, allows safety and preserves privacy. The DP-3T initiative, e.g., has been taken as reference by Google and Apple for implementation on their smartphones (with some differences, however). The TCN coalition developed an alternative open solution.

Several protocols exist, thus, and tens of implementations are already under development or readily available. Many countries are trying to find an effective solution that can meet the citizens' acceptance. Indeed, it is hard to enforce contact tracing due to technical issues and privacy concerns. These are discussed daily on the Internet, but how effective contact tracing can be? Good or Bad? I will show the results of a few experiments I have conducted on my own.

Before moving on to take a look at my own experiments, I want to state that these are only for illustrative purposes and they do not represent an attempt to forecast or suggest guidelines. A necessary read, for those who are interested, is the scientific paper from Ferretti et al. appeared on Science in March 2020.

Now, let us see how contact tracing works in a simulated scenario.

A DISCRETE-TIME MULTI-AGENT MODEL

The effect of contact tracing can be discussed theoretically and some mathematical models can be derived as done in the paper by Ferretti et al. But I wanted to build up an experiment that models a population in terms of "agents", to analyze how the parameters affect the beneficial effects of contact-tracing.

The simulation works this way: there is a "population" of thousands simple agents. Each one of these represents a human and behaves differently depending on its state:

  • healthy: moves freely but can be infected

  • incubating: can spread the virus without knowing

  • ill: has symptoms and gets quarantined/cured

  • dead

  • recovered from the illness: is again free and won't be reinfected

For simplicity, I imposed that only incubating individuals can spread the virus, and ill individuals are well contained. Healthy individuals can be infected and when they are, they start the incubation period. After a few days of incubation, the symptoms arrive and one knows to be ill, then it is put into quarantine and gets cured. In this phase it cannot spread the disease anymore. Ill individuals have a certain probability of recovery or death. For simplicity, in this computational model I assume recovered individuals are immune (however, "as of 24 April 2020, no study has evaluated whether the presence of antibodies to SARS-CoV-2 confers immunity to subsequent infection by this virus in humans." [source: WHO]).

The image below tries to depict what the system looks like taking a snapshot at certain moment.

We ca