Models

In order to reproduce the COVID-19 spread with accuracy it is necessary to model the simulated environment in a realistic manner. EpiGraph includes four different models that are executed in coordination: the epidemic model that provides the COVID-19 propagation behaviour, the social model that depicts the characteristics and relationships of individuals within the population, the transportation model that considers the movement of the individuals, and the environmental model that represents the ambiental elements (weather, pollution, etc.) that modulate the spread of the infection. 

 

  • Epidemic model design. We use the SEIR++ model with 17 different states to include states for latent, asymptomatic, and dead. We added an additional hospitalized state and vaccination or anti-viral therapies. This model captures the mechanism by which susceptible individuals get infected and go through the different stages of the infection. The infectious period has three phases with different characteristics, which may affect the dissemination of the virus: pre-symptomatic infection, primary stage of symptomatic infection, and the second stage of symptomatic infection. We also consider the asymptomatic stage. Note that each stage has a related different R0 value. The time each individual spends in a given state is generated following a normal distribution to simulate the time ranges specific to each stage of the infection, so each individual has different phase lengths. We adopt most of the concrete values for the model parameters from the existing literature. 

  • Social model design. We developed a social model for the population under study, including the patterns of contact between individuals within this population. The social model is represented via an undirected connection graph and can capture heterogeneity features at the level of both the individual and each of his/her interactions. We use contact information from social networks to realistically approximate these connections. We allow for customizing individual interaction behavior based on the day of the week and the time of day. In this way, we model social structures such as companies, schools, or groups of stay-at-home parents and retired people that are interacting in education programs, hobby classes, kids’ schools or any other kind of activities that make them come in contact with each other. At the level of the individual, we allow for the modeling of characteristics such as age, gender, and race. In the following figure we can see an example of a reduced contact network used in EpiGraph.

  • Transportation model design. The transport component models the daily commute of individual to neighboring cities (inter-city movement) and the long-distance travels for several days that represent commute of workers that need to reside at different locations or people that move at any distance for vacation purposes. The people mobility model uses geographical information extracted from Google using the Google Distance Matrix API service.

 

  • Environmental model design. We use of meteorological forecasts and air pollution levels (Smart Environments) allows for improved simulation given that these values affect the ability of the virus to be propagated. As future work, an important project research line is to enhance the social model with a detailed environment design. With the implementation of the Internet of Things, more and more elements of our common life can be tracked and processed. This data provides very valuable information that can be used for increasing the accuracy of EpiGraph. For instance, in urban environments (Smart Cities) traffic, public transport and pedestrian conditions can be used to model social interactions. Data collected from hospitals or pharmacies will contribute to model the spread of the epidemic. A more detailed analysis of social networks allows for the consideration of geolocalization data as well as providing additional information about the number of infected individuals.