Novel approach to extract epidemiological information from waves in epidemic's profiles

In this paper, we develop a novel mathematical framework based on the Kermack- McKendrick model to extract epidemiological parameters from real temporal profiles consisting of waves. The approach's key feature is the ability to obtain all model parameters from the geometry of the wave of interest. We propose three new quantities to measure the negative impact of the epidemic wave on a specific population, called <i>Fraction of endemicity</i>, <i>Severity</i>, and <i>Asymmetry</i>. These three measures, along with a refined definition of the <i>basic reproduction number</i>, provide crucial epidemiological information. We demonstrate analytically that there is an equivalence among these quantities, and such equivalence gives a way of obtaining all parameters in the model since the <i>Asymmetry</i> of a real epidemic wave is easily computed. This is the heart of the novel methodology we introduce. The framework is suitable for public health decision support, as its implementation does not rely on complex mathematical tools. We present several case studies to illustrate the simplicity of the framework as well as the distinct aspects of its implementation. In all examples investigated, the numeric solution obtained with the parameterized model shows good agreement with the available data.