Network modelling of SARS-Cov-2 transmission

SEIR network model

Modelling how infectious diseases spread is a complex process that involves not only understanding the virus itself, but also the behaviour of the people who are transmitting it. Rafael Villanueva of the Polytechnic University of Valencia has been leading a project that aims to ramp up the capabilities of his network models to provide a deeper understanding of the COVID-19 pandemic and eventually provide advice on the best vaccination strategies for the near future.

Rafael Villanueva, a researcher in interdisciplinary mathematics at the Modelling and UNcertainty QUantification group (MUNQU) at the Polytechnic University of Valencia, specialises in modelling infectious diseases. His previous experience has led to close working relationships with doctors working on public health issues, especially on the topic of how different vaccines provide protection to populations.

With this knowledge of using mathematical models in the field of epidemiology, it is no surprise that with the onset of the COVID-19 pandemic, he was quick to offer up his expertise to help solve this global issue. “Everyone in my team here at the Polytechnic University of Valencia was very keen to work on this topic,” says Villanueva. “Some of them suggested trying to make predictions about how the disease might evolve over time, especially here in Spain.”

Rafael Villanueva, a researcher in interdisciplinary mathematics at the Modelling and UNcertainty QUantification group (MUNQU) at the Polytechnic University of Valencia

Rafael Villanueva

After making themselves familiar with the ongoing and rapidly evolving research on COVID-19, the team began integrating these findings into their epidemiological models. Over time, the models became more and more complex as more information came to light from various fields of research. One of the models used by the team is known as SEIR. The SEIR model assumes that all individuals in a population are of one of four states: Susceptible, Exposed, Infected or Recovered (or Removed). “With our network model, we simulate each individual as a node,” explains Villanueva. “Connections between these nodes are known as edges. This means that two nodes that are joined by an edge can potentially transmit the disease to each other.”

These types of models have attracted a lot of interest since the outbreak of the COVID-19 pandemic but, as Villanueva and his team found out, they become computationally expensive when larger numbers of individuals are placed into the network. Having reached the capacity of their in-house computers, they applied to PRACE for computing time on Europe’s fastest supercomputers to continue exploring their work.

“What we found when working with smaller networks on our own computers was that certain behaviours that we know to exist, such as the seasonality of infectious diseases, do not arise naturally in our simulations,” explains Villanueva. “This led to us applying for PRACE’s fast-track call for research on COVID-19 so that we could use our models on much larger computers and create more accurate predictions.”

The SEIR network model assumes that all individuals in a population are of one of four states: Susceptible, Exposed, Infected or Recovered (or removed). Each individual is represented as a node, and nodes connected by “edges” can transmit the infection to each other.

Seasonal cycles are common in infectious diseases, with many of the more common viruses such as cold, influenza and rotavirus being more prevalent in winter. Why these patterns arise is poorly understood, but they represent significant oscillations in infection levels in populations and therefore must be taken into account. This seasonality emerges naturally in the kind of model being used by Villanueva, but only when using around one million nodes or more.

The PRACE project, entitled “Calibration of the parameters of a network model for studying the transmission dynamics of the SARS-Cov-2”, is helping to calibrate the parameters of the model by running around 50 000 iterations of a simulation. This will eventually allow patterns such as seasonality to emerge in the model, and also potentially show new behaviours in the transmission of the disease. Villanueva and his team aim to eventually run their simulations with over one million nodes in their network, but are currently running it with around 600 000.

Once the model has been calibrated, it will be used to examine how a potential vaccine might work to help suppress the pandemic. Not all vaccines act upon people in the same way; while some are able to both protect the person receiving it and block transmission to others – the best possible scenario – other vaccines will only provide protection to the person who receives it, and will not necessarily stop them from carrying and spreading the disease. Villanueva and his team are examining a range of scenarios in between these two extremes, and looking at how this will affect the number of people being hospitalised. In terms of feeding the results of their work into actionable steps for public health, Villanueva and his team hope that their simulations will be able to point towards the best possible strategy for vaccinating people in order to avoid highly crowded hospitals and high death rates.

The MUNQU Team

The MUNQU Team

“In some of our previous studies on other diseases, we have even been able to give concrete recommendations that doctors can implement in their daily work,” he says. “However, in this case, what we are aiming to do is to provide as much information as possible to policymakers so that they can make the appropriate decisions. Of course, we are not the only group working in this field, so those people will have to examine several sources of information before coming to any decision.”

Villanueva is grateful to PRACE for the allocation of 750 000 core hours on the Jülich Support for Fenix CPU at the Jülich Supercomputing Centre in Germany that his team received, without which he believes the work he has carried out would have been impossible. “I have never had a lot of luck with these kinds of proposals in the past, so I was very surprised when ours was accepted!”, he says. “The mentoring system they had in place was very useful to us, as we were able to ask our mentor Filipe Guimaraes any questions which he always helped us with very quickly. We certainly would not have been able to do some parts of this work without his assistance.”

This article was also published in PRACE Digest 2020.

More information:
http://munqu.webs.upv.es

Resources awarded:
750 000 core hours on Jülich Support for Fenix CPU at the Jülich Supercomputing Centre in Germany

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