Simulating COVID-19 at large scale

EpiGraph is a parallel simulator that performs realistic stochastic simulations of the propagation of the COVID-19 virus across wide geographic expanses. EpiGraph was originally designed in the Computer Architecture research group of University Carlos III and later, developed further with the collaboration with Barcelona Supercomputing Center.

The current implementation of EpiGraph includes functionalities for modeling via a realistic interconnection network based on actual individual interactions extracted from social networks and demographical data. This network includes the characteristics of each individual (student, worker, elderly and stay-at-home), their relationships at work, school, home and during leisure time, and a transportation model which simulates the spatial dynamics of the virus’ propagation over-large scale areas. EpiGraph also includes a model of the interaction between COVID-19 spread and climate and meteorological factors, such as temperature, atmospheric pressure and humidity levels.

To date, we have evaluated the different enforcement policies that can be combined:

  • Use of face masks with different levels of protection used by the whole population of specific collectives. 
  • Asymptomatic detection by test kits. 
  • Herd immunity threshold. 
  • School closures, where all the students maintain family and leisure time contact, but do not attend school. 
  • Transportation restrictions, with modelling of scenarios for the restriction of both short and long distance trips.
  • Working from home, where a given percentage of workers stay at home.
  • Self-distancing, where leisure-time connections are avoided by all the individuals. 


Simulating the spread in Spain

The following figure shows a preliminary validation of EpiGraph. Red bars represent the accumulated official number of deaths in Comunidad de Madrid until 8th of April. The blue line represents the average value of five different simulations. The green lines correspond to the standard error.  Simulation day 10 is equivalent to 16th of March where partial enforcement  policies are applied, including closure of schools, working from home for 65% percent of businesses, social distancing and travel restrictions – all reflecting the real-life policies that have been enforced in Spain. At simulation day 24 100% of  the companies are closed. The simulation is limited to the city of Madrid, and the following surrounding major cities of Alcalá de Henares, Alcobendas, Alcorcón, Fuenlabrada, Getafe, Leganés, Móstoles and Parla – a total of 5,018,241 inhabitants. The simulated values have been scaled to the current population of the community (6.6 million). The current version of the simulation only considers the deaths that occur in hospitals. According to some sources of data, the actual number of deaths could be up to 30% higher. 

The following animations show different stages of the simulation of an outbreak of COVID-19 for the 62 most populated cities in Spain comprising a total of 20 million inhabitants. We have used censal data from the Spanish Office for Statistics and the Spanish Ministry of Health for the social modelling. All the simulations show the total number of infected including symptomatic and asymptomatic cases. Note that these numbers are much bigger than the number of reported cases. The beginning of week 1 corresponds to 17th of March of 2020. 

In the animation below two scenarios are compared:

  • Baseline: no restrictions are taken, the virus freely propagates throughout the whole simulation
  • Social enforcement policies: starting from week 1, including closure of schools, working from home, social distancing and travel restrictions – all reflecting the real-life policies that have been enforced in Spain.

The following animation shows the surgence of new peaks in COVID-19 propagation. At week 1, social enforcement policies are introduced, including the closing of schools, working from home, social distancing and travel restrictions. At week 14*, 10% of the population are permitted to return to work with the whole population takes prevention measures to avoid the propagation.  


The next animation is similar to the previous one, but at week 16*, 10% of the population are permitted to return to work but no prevention measures are taken. We are currently refining the model to consider more factors and extending the simulation to Europe. 

*Note that this week is an example return date and not based on real plans.


Simulating the spread in Europe

The following figure shows the cities used to perform the simulation in Europe. In total, there are 612 cities that correspond to the largest cities in Europe with an aggregated population of 195 million people. Each city was modeled using related information obtained from Eurostat and other European offices. 



The short-term effects we are interested in are:

  • Studying of the efficiency of enforcement policies for slowing the spread of the epidemy.
  • Recommending policies for minimizing the number of infections in the short term (in order to reduce the spread the disease) as well as the number of serious and critical cases, by means of taking specific measures with certain population segments.

The medium-term effects we are interested in are:

  • Which enforcement policies should be taken to reduce the probability of future peaks?
  • What is the impact of climate conditions on the epidemic outcome?
  • What measures should be maintained and for how long, after we flatten the curve?
  • Does border closing affect propagation?


EpiGraph strengths for the analysis of COVID-19 expansion

  • EpiGraph models every single individual of the population. It is possible to include personal characteristics of each individual such as state of health, occupation, age, genre, existing pathologies, etc. and use them in the simulation process.
  • Distributed and scalable simulator. We implement a scalable, fully distributed simulator in MPI. Currently EpiGraph can be executed using hundreds of compute nodes and can perform simulations of a complete season for environments with hundreds of millions inhabitants. Currently we are performing European-scale simulations of the COVID-19 propagation. 
  • Realistic simulations. We have validated the results of the simulations with other simulators as well as real data obtained from NYSDOH and the influenza surveillance data obtained from the SISSS (Spanish Influenza Sentinel Surveillance) System corresponding to the 2010-2011 influenza season in Spain. 
  • Study of different scenarios. EpiGraph permits the simulation of time-dependent R0 values. As such we are able to analyze the effect of changes in climate on COVID-19 propagation, for example the effect of warmer climate conditions (related to the arrival of the spring) on virus spread. In addition, we analyse and compare the impact of different potential vaccination policies on managing the virus’ dissemination process.


The team coordinated by David Expósito Singh comprises groups from University Carlos III de Madrid (UC3M) and Barcelona Supercomputing Center (BSC).

  • At UC3M: David Expósito Singh, Jesús Carretero and Diego Fernández Olombrada
  • At BSC: María-Cristina Marinescu


  • At Wuhan Center for Disease Control & Prevention, China International Joint Research Center of Green Communications and Networking: Professor Xiaohu Ge

Former members

  • Florin Isaila, Gonzalo Martín



This work has been recently funded by Instituto de Salud Carlos III, Ministry of Health and Innovation under the COV20/00935. Additionally, this work has been partially funded by the Spanish Ministry of Science and Education under the MEC 2011/00003/001, TIN2010-16497 and TIN2016-79637-P contracts. We also would like to thank Agencia Estatal de Meteorología (AEMET) for providing meteorological data of Spain.


Other projects

The list of projects developed in ARCOS research group can be accessed here.