An SIR model with viral load-dependent transmission

Predictability of viral load dynamics in the early phases of SARS-CoV-2 through a model-based approach

A pipeline to evaluate the evolution of viral dynamics based on a new model-driven approach has been developed in the present study. The proposed methods exploit real data and the multiscale structure of the infection dynamics to provide robust predictions of the epidemic dynamics. We focused on viral load kinetics whose dynamical features are typically available in the symptomatic stage of the infection. Hence, the epidemiological evolution was obtained by relying on a compartmental approach characterized by a varying infection rate to estimate early-stage viral load dynamics, of which few data are available. We tested the proposed approach with real data of SARS-CoV-2 viral load kinetics collected from patients living in an Italian province. The considered database refers to early-phase infections, whose viral load kinetics have not been affected by the mass vaccination policies in Italy.

Modelling contagious viral dynamics: a kinetic approach based on mutual utility

The temporal evolution of a contagious viral disease is modelled as the dynamic progression of different classes of population with individuals interacting pairwise. This interaction follows a binary mechanism typical of kinetic theory, wherein agents aim to improve their condition with respect to a mutual utility target. To this end, we introduce kinetic equations of Boltzmann-type to describe the time evolution of the probability distributions of the multi-agent system. The interactions between agents are defined using principles from price theory, specifically employing Cobb-Douglas utility functions for binary exchange and the Edgeworth box to depict the common exchange area where utility increases for both agents. Several numerical experiments presented in the paper highlight the significance of this mechanism in driving the phenomenon toward endemicity.