Simulating the spread of COVID-19 via spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion (2005.05320v1)

Abstract: We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitative agreement between the simulated forecast of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data collected at the municipality level. Additional simulations exploring alternative scenarios for the relaxation of lockdown restrictions suggest that reopening strategies should account for local population densities and the specific dynamics of the contagion. Thus, we argue that data-driven simulations of our model could ultimately inform health authorities to design effective pandemic-arresting measures and anticipate the geographical allocation of crucial medical resources.

Simulating the Spread of COVID-19 with a Spatially-Resolved SEIRD Model

This paper presents a sophisticated application of mathematical modeling to simulate the propagation of the COVID-19 pandemic using a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) model. Leveraging partial differential equations (PDEs) and heterogeneous diffusion, this model aims to account for spatial and temporal variability in the pandemic's spread, informed by human behaviors and geographical features. The chosen region for evaluation, Lombardy in Italy, underwent severe COVID-19 impacts in early 2020, offering a rich dataset to validate the model's fidelity.

The modeling framework advances prior compartmental approaches by introducing PDEs to capture the continuous dynamics of infectious spread, incorporating an inhomogeneous diffusion based on natural and societal heterogeneities such as geographic barriers and transport networks. This allows for a deterministic representation of local movement as the limit of a Brownian motion.

Numerical Implementation and Model Calibration

The deployment utilized finite-element spatial discretization, focusing on Lombardy's triangular mesh to simulate pandemic dynamics meticulously. Following a preliminary estimation using a 0D SEIRD model, parameters were refined iteratively to match epidemiological data with emphasis on the deceased subgroup for calibration. The authors argue that targeting mortality data provides a more accurate understanding of model parameters due to known discrepancies in infection reporting.

Results and Insights

The model exhibited strong qualitative alignment with reported infection dynamics across Lombardy's municipalities. The spatial simulations highlighted the spread from initial epicenters like Lodi into Milan, affirming the predictive power of PDE-based models over continuous domains. A key implication from these simulations is the ability to evaluate differing reopening scenarios. Simulations suggested that retaining lockdown measures in high-density areas like Milan could significantly curtail further outbreaks, offering strategic insights for pandemic response tailored to local demographics and contagion patterns.

Discussion and Future Directions

The paper recognizes its early-stage model and suggests expansions such as incorporating dynamic and non-local effects, improving parameter updates via data assimilation, and enhancing boundary condition realism. Future iterations could encompass more detailed population structures, hospitalization, and socio-economic variables to enrich decision-making capacity for health authorities.

The implications of employing advanced mathematical modeling frameworks like this SEIRD-PDE fusion extend beyond COVID-19, presenting cogent methodologies to anticipate and understand infectious dynamics in diverse contexts. As data accumulates and model refinements continue, this approach could serve as a robust tool for predictive epidemiology, informing resource allocation and containment strategies authored to regional needs.