Analytical approach for structural engineering design improves COVID-19 fatality monitoring

Epidemiological models for predicting the spread of the COVID-19 have largely fallen into two types of mathematical approaches. Differential equations using compartments of the population, such as people who are infected or deceased, are limited in their predictive ability. Agent-based models draw on rules to simulate autonomous people but often lack reliable input data and are computationally expensive.

Ukaj et al. introduce an approach for modeling COVID-19 fatality trends based on convolutional integro-differential equations from Boltzmann’s hereditary mechanics. Replacing statistical reasoning underlying most models with assumptions drawing on viral load and its effect on populations over time, the approach reduces model errors by up to 98% compared to the Kermack–McKendrick theory, the mainstay of epidemiological modeling.

It marks one of the first adaptations of structural engineering design for epidemiology.

“If you put a load on a concrete beam, this beam will bend. However, if the load sustains, the bending will, over time, go on—less and less, but strictly speaking, it will never stop,” said author Christian Hellmich. “The actual bending behavior depends on the load history applied to the beam. And interestingly, the same holds if one replaces the notions of ‘bending’ with ‘fatality trend,’ and notion of ‘load’ with ‘viral load.’”

The coefficient of determination calculated between the group’s model predictions and recorded data ranges from 94% to 100%. To date, equation-based epidemic modeling has yet to achieve such precision.

Hellmich hopes the group’s work inspires others to explore more cross-disciplinary approaches to modeling phenomena. The group looks to expand their findings to COVID-related intensive care cases and one day analyze systems of integro-differential equations.

Source: “Toward “hereditary epidemiology”: A temporal Boltzmann approach to COVID-19 fatality trends,” by Niketa Ukaj, Stefan Scheiner, and Christian Hellmich, Applied Physics Reviews (2021). The article can be accessed at https://doi.org/10.1063/5.0062867 .