Understanding COVID-19 Epidemics: A Multi-Scale Modeling Approach
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COVID-19 was declared a pandemic by the World Health Organization in March 2020 and, since then, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading and control under different scenarios. In this chapter, two different approaches to model the spread of COVID-19 are presented. The model frameworks are described and results are presented in connection with the current epidemiological situation of vaccination roll-out. This chapter is structured as follows. Section 2 presents the stochastic SHARUCD modeling framework developed within a modeling task force created to support public health managers during the COVID-19 crisis. As an extension of the basic SHAR (Susceptible-Hospitalized-Asymptomatic-Recovered) model, the SHARUCD models were parameterized and validated with empirical data for the Basque Country, Spain, and have been used (up until now) to monitor COVID-19 spreading and control over the course of the pandemic. Section 3 introduces the kinetic theory of active particles (KTAP) model for the spread of a disease. With an exploratory analysis, we present a possible way to deal with heterogeneity and multiscale features. Section 4 concludes this work, with a discussion on both models and further research perspectives description.