Kinetic models for epidemic dynamics with social heterogeneity

We introduce a mathematical description of the impact of the number of daily contacts in the spread of infectious diseases by integrating an epidemiological dynamics with a kinetic modeling of population-based contacts. The kinetic description leads to study the evolution over time of Boltzmann-type equations describing the number densities of social contacts of susceptible, infected and recovered individuals, whose proportions are driven by a classical SIR-type compartmental model in epidemiology. Explicit calculations show that the spread of the disease is closely related to moments of the contact distribution. Furthermore, the kinetic model allows to clarify how a selective control can be assumed to achieve a minimal lockdown strategy by only reducing individuals undergoing a very large number of daily contacts. We conduct numerical simulations which confirm the ability of the model to describe different phenomena characteristic of the rapid spread of an epidemic. Motivated by the COVID-19 pandemic, a last part is dedicated to fit numerical solutions of the proposed model with infection data coming from different European countries.

Automated summary

The study combines epidemiological dynamics with kinetic modeling of population-based contacts to introduce a mathematical description of the impact of the number of daily contacts in the spread of infectious diseases. The kinetic model clarifies how a selective control can be assumed to achieve a minimal lockdown strategy by reducing individuals undergoing a very large number of daily contacts. Numerical simulations confirm the model's ability to describe different phenomena characteristic of the rapid spread of an epidemic, while the model is also fit to infection data from various European countries in response to the COVID-19 pandemic.