ABSTRACT
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. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
ABSTRACT
We investigate models to describe respiratory diseases with fast mutating virus pathogens such that after some years the aquired resistance is lost and hosts can be infected with new variants of the pathogen. Such models were initially suggested for respiartory diseases like influenza, showing complex dynamics in reasonable parameter regions when comparing to historic empirical influenza like illness data, e.g., from Ille de France. The seasonal forcing typical for respiratory diseases gives rise to the different rich dynamical scenarios with even small parameter changes. Especially the seasonality of the infection leads for small values already to period doubling bifurcations into chaos, besides additional coexisting attractors. Such models could in the future also play a role in understanding the presently experienced COVID-19 pandemic, under emerging new variants and with only limited vaccine efficacies against newly upcoming variants. From first period doubling bifurcations, we can eventually infer at which close by parameter regions complex dynamics including deterministic chaos can arise.