Due to the COVID-19 pandemic, I was interested in how a virus would spread in a transport network. It is particularly interesting to see how central hubs contribute to spread the infection and which times are the most dangerous to travel.

In order to observe how a virus spreads in a network, in this project I run a one-day simulation based on the passenger flow.

In this project, I have used the data of the Renfe Cercanias transport network in Madrid (Spain), but you can run the code using your own network (bus, flights, ...).

Turnstiles data, route timetables and station locations:

• http://crtm.maps.arcgis.com/home/item.html?id=1a25440bf66f499bae2657ec7fb40144
• https://data.renfe.com/dataset/volumen-de-viajeros-por-franja-horaria-madrid

At the time that I am writing this text, there are some limitations in the above data:

• There is no data for the newest station: Mirasierra-Paco de Lucía.
• There is no data in two lines: C-3a and C-4b.
• Line C-9 do not have turnstiles, thus there is no data of any station.

Hence, after excluding those stations with missing data, the network looks like this:

I have used the library Mesa to implement an Agent Based Model to simulate the flow of passengers in the network.

In order to simulate the flow in a realistic way, I have used the turnstiles data of each station at each time. Based on such data, each station (and also each line) has a certain in-weight and out-weight (depending on the number of incoming and outcoming passengers).

At each time step, a certain number of passengers join the network randomly:

1. Depending on the time, N passengers join the network. That is, if it is a peak hour, more passengers will join it.
2. Each passenger is assigned to a station randomly (origin station) depending on the in-weight of the station/time.
3. Each passenger randomly goes to a platform in the station depending on the weight of the platforms. Note that the weight of a platform depends on the sum of in-weights of the next stations.
4. Finally, the passengers waits in the platform until a train arrives.

The passengers who are in a train:

1. Leave the network (arrival to destination) depending on the out-weight of the station and time.
2. Stay in the train or change to other platform depending on the weight of the platforms.

You can see a short animation of the passengers flow (note that some nodes suddenly become blue/gray when a train arrives to the node and takes the passengers who are waiting for it): ./images/flow-sim.gif

I have used a SEI Model which consists of 3 states:

• Susceptible (S): a healthy person who can be infected.
• Exposed (E): incubation period during which individuals have been infected but are not yet infectious themselves.
• Infected (I): people who are capable of infecting susceptible individuals.

Once a susceptible individual (state S) has been infected by another passenger (state I), his/her new state changes from S to E. Since I am planning to run a one-day simulation, I do not use a SEIR Model (which includes the state Recovered).

Then, an infected individual may infect others with a certain probability p to susceptible people who are in the sample place:

• When s/he is waiting for a train in a platform.
• When s/he is traveling in a train.

Here is an animation where you can see the total number of infected/exposed passengers in the network: ./images/infect-sim.gif

There are some additional constraints to take into account:

• A passenger cannot join a station/platform whether there are no more expected trains or the next train comes in more than 30 minutes (feel free to change it for your own network).
• A passenger may change to other platform, but they cannot change to a platform of the same line. This allow me to force that passengers do not do "useless transfers".
• In my network, I limited that each passenger can make one only transfer to another line.
• In real life, if there are only 2 passengers in a platform, the most likely is that one cannot infect to the other (due to the physical separation between them). However, this model is simple, so they may get infected anyway.

Please, take a look to the notebook NetworkSimulation for further details about parameters and additional results.

After running the simulation, I noticed that the most infection happen not only in central hubs (as I expected) but also in stations where passengers wait for a long time:

Here are the top 20 stations with more infections:

Furthermore, it is interesting to see how the most infections happen during peak hours:

You can see the code details in the folder notebooks