# Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics

arXiv: https://arxiv.org/abs/2110.00293 · HTML: https://mlsanity.com/paper/2110.00293/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread](https://mlsanity.com/paper/2206.12625/) (2022)
- [Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling](https://mlsanity.com/paper/2210.09081/) (2022)
- [A data augmentation strategy for deep neural networks with application to epidemic modelling](https://mlsanity.com/paper/2502.21033/) (2025)
- [Augmented data and neural networks for robust epidemic forecasting: application to COVID-19 in Italy](https://mlsanity.com/paper/2510.09192/) (2025)

## Abstract (arXiv)

In this survey we report some recent results in the mathematical modeling of epidemic phenomena through the use of kinetic equations. We initially consider models of interaction between agents in which social characteristics play a key role in the spread of an epidemic, such as the age of individuals, the number of social contacts, and their economic wealth. Subsequently, for such models, we discuss the possibility of containing the epidemic through an appropriate optimal control formulation based on the policy maker's perception of the progress of the epidemic. The role of uncertainty in the data is also discussed and addressed. Finally, the kinetic modeling is extended to spatially dependent settings using multiscale transport models that can characterize the impact of movement dynamics on epidemic advancement on both one-dimensional networks and realistic two-dimensional geographic settings.