The Use of Triangular Norms in Epidemiological Models: A Comparative Study Using COVID-19 Data

Abstract

In this manuscript we use triangular norms to model contact between susceptible and infected individuals in the susceptible-infected-recovered (SIR) epidemiological model. In the classical SIR model, the encounter between susceptible and infected individuals is traditionally modelled by the product of their densities ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$SI$</tex-math></inline-formula> ). That is, the encounter is modelled by the product t-norm. We use the COVID-19 data and extended versions of the SIR model whose encounters are modelled by four triangular norms, namely, product, minimum, Frank and Hamacher t-norms, to analyze the scenario in three countries: Germany, Italy, and Switzerland. We compare all versions of the SIR model based on these triangular norms, and we analyze their effectiveness in fitting data and determining important parameters for the pandemic, such as the basic and effective reproduction number. In addition, Frank and Hamacher triangular norms present an auxiliary parameter that can be interpreted as an indicator of control measure, which we show to be important in the current pandemic scenario.