Guillermo Lorenzo

Data-driven mechanistic models to forecast COVID-19 outbreaks

The COVID-19 pandemic has led to a surge of interest in mechanistic modeling and simulation of infectious diseases to forecast outbreak evolution. These mathematical models are usually based on a classical compartmental paradigm, which describes the temporal dynamics of disease spread over a certain region of interest whose population is distributed in different compartments according to disease status (e.g., susceptible, exposed, infected, recovered, deceased). These models and other recent model-naïve, purely data-driven statistical approaches have been useful in monitoring and controlling COVID-19 outbreaks.

To contribute to the global effort in understanding and predicting the spread of COVID-19, this research has four main objectives: 
    (1) defining mathematical models that specifically account for the temporal mechanisms of  COVID-19  infection based on classical compartmental formulations,
    (2) extending these models to include key spatial mechanisms (e.g., clustering towards highly-densed areas, mobility of individuals),
    (3) constructing computational methods to efficiently and accurately calibrate and solve these mathematical models using longitudinal epidemiological data,
    (4) investigating the use of simulation results to inform the decision-making of public health interventions (e.g., design levels of restriction, timing and magnitude of lockdowns, regional allocation of medical resources).
Figure. Model forecast of COVID-19 spread in Lombardy. (A) Main areas affected by the pandemic in Lombardy. (B) Initially, the main affected areas are Lodi and Cremona and, to lesser extent, Bergamo and Brescia. (C–E) Our model predicts increasing exposures in Bergamo and Brescia. The outbreak in Lodi soon moves north into the Milan metro area, where it further spreads despite the lockdown restrictions. (F) The model also predicts that governmental restrictions eventually succeed in reducing the exposure to the disease, which is faster in Brescia and Bergamo than in Milan. (G) Cumulative curves of infections according to reported data (dots) and simulations (dashed lines) for the three main areas of contagion: Bergamo, Brescia, and Milan. The model has been calibrated to match the data reported for the deceased subgroup, resulting in a forecast of a larger number of infections. To highlight the qualitative agreement of our simulations, we also show the numerical results scaled to match the order of magnitude of the reported infectious data (solid lines). Reproduced with permission from Viguerie et al. (2021),  Appl Math Lett, 106617.


Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion

Alex Viguerie, Guillermo Lorenzo, Ferdinando Auricchio, Davide Baroli, Thomas J.R. Hughes, Alessia Patton, Alessandro Reali, Thomas E. Yankeelov, Alessandro Veneziani

Applied Mathematics Letters, 2021, p. 106617

Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study

Alex Viguerie, Alessandro Veneziani, Guillermo Lorenzo, Davide Baroli, Nicole Aretz-Nellesen, Alessia Patton, Thomas E. Yankeelov, Alessandro Reali, Thomas J. R. Hughes, Ferdinando Auricchio

Computational Mechanics, vol. 66(5), 2020, pp. 1131–1152