Optimal control of epidemic spreading in the presence of social heterogeneity.

The spread of COVID-19 has been thwarted in most countries through non-pharmaceutical interventions. In particular, the most effective measures in this direction have been the stay-at-home and closure strategies of businesses and schools. However, population-wide lockdowns are far from being optimal, carrying heavy economic consequences. Therefore, there is nowadays a strong interest in designing more efficient restrictions. In this work, starting from a recent kinetic-type model which takes into account the heterogeneity described by the social contact of individuals, we analyse the effects of introducing an optimal control strategy into the system, to limit selectively the mean number of contacts and reduce consequently the number of infected cases. Thanks to a data-driven approach, we show that this new mathematical model permits us to assess the effects of the social limitations. Finally, using the model introduced here and starting from the available data, we show the effectiveness of the proposed selective measures to dampen the epidemic trends. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

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.

Photosynthesis, Ribulose-1,5-bisphosphate Carboxylase, Electron Transport, and Ribulose 1,5-Bisphosphate of Virescent and Normal Green Wheat Leaves.

CO(2) gas exchange, ribulose-1,5-bisphosphate, and electron transport have been measured in leaves of a yellow-green mutant of wheat (Triticum durum var Cappelli) and its wild type strain grown in the field. All these parameters, expressed on leaf area basis, were similar in both genotypes except electron transport which was more than double in the wild type. These results, treated according to a recent photosynthesis model for C(3) plants, seem to indicate that the electron transport rate of mutant leaves is not sufficient to support the carboxylation derived through both the assimilation rate and the in vitro ribulose-1,5-bisphosphate carboxylase activity. It is suggested that under our experimental conditions photosynthetic electron transport is not the sole energy-dependent determinant of ribulose-1,5-bisphosphate regeneration in the mutant.