Modeling the spatio-temporal spread of COVID-19 via a reaction-diffusion system
Malú Grave (UFF)

The COVID-19 outbreak in 2020 sparked significant interest in mathematical models of infectious diseases. These models categorize the population into compartments based on characteristics. While often expressed as ordinary differential equation (ODE) models, which depend solely on time, recent research has explored partial differential equation (PDE) models, particularly reaction-diffusion models that incorporate spatial variation in epidemics. These PDE models, within the Susceptible, Infected, Exposed, Recovered, and Deceased (SEIRD) framework, have shown promise in describing COVID-19’s progression. However, the rapid movement of people over long distances can result in nonlocal disease transmission, a phenomenon not well represented by diffusion alone. In contrast, ODE models can account for this by treating different regions as network nodes, connected by edges to represent nonlocal transmission. To address these complexities, a reaction-diffusion PDE model is developed with an integrated network structure. This approach aims to enhance our understanding and prediction of COVID-19 contagion dynamics in a more realistic and comprehensive way.