Modelling the disease spread
Modelling the disease spread.
The results of the first 50 days of infection spread modelling (cities and directions of infection spread).
Link to video presentation from the OpenDataDay conference (Russian only)
The approach is based on combining two general strategies to infection modelling: using Susceptible-Infectious-Recovered/Removed (SIR) model for the city-level spread, and simultaneously modelling the spread of the decease through the air-traffic network.
Algorithm pseudocode:
INFECTED_CITIES
with Wuhanday
in simulation_days
infected_city
in INFECTED_CITIES
:
airports
of the infected_city
connections
for the airports
susceptible_city
in connections
:
susceptible_city
susceptible_city
is infected - update INFECTED_CITIES
day
To model the spread of infection within a particular city we use a homogeneous Susceptible-Infectious-Recovered/Removed (SIR) model with several assumptions. Although quite simplistic, the model proves to be reasonable for approximating the COVID-19 infection spread. There are several reasons for this efficiency:
The major idea that we've implemented to address the changes in the infection rate due to social distancing and quarantine measures is dynamically modelling the reproduction nunmber R. The idea is straightforward - adjust R in response to the preventive measures. As a baseline, we took the Wuhan example of preventive measures and their approximate timelines.
Finally, for each infected city we run an SIR model to get the number of infected people for all days of simulation.
To model the infection spread through the airline traffic network we need to calculate the probability that a given susceptible city would be infected by its neighbouring infected city on a given day.
We consider a city infected if at least one infected plane landed in this city. Hence, first we need to calculate the probability that the plane coming from the infected city is infected itself:
,
where I - number of infected in the city, N - total population of the city.
Next, we can calculate the probability that the city is infected:
where f - flights from city per day.
As a result, we recalculate the probabilities of infection spread based on the estimated number of the infected population in the infected cities. That approach proved to be surprisingly accurate and was able to "predict" major COVID-19 outbreaks, e.g. in Western Europe or the USA.