arXiv subjects

Elisa Paparelli

Publications and source records attributed to Elisa Paparelli.

3 recordsLinked to original sources

arXiv2026

Optimal control on a heterogeneous SI epidemic model

This work addresses an optimal control problem for a SI epidemic model incorporating heterogeneities in resistance and viral load at the population level. Building upon the heterogeneous SI framework developed in [1], a minimization problem constrained to the macroscopic counterpart of the SI dynamics derived therein is proposed. Unlike traditional optimal control problems in homogeneous epidemic models, the present approach focuses on an optimal control problem that accounts for population heterogeneity, offering insights from a microscale perspective. The contribution aims to minimize the final size of the infection within a finite time horizon by developing a pharmaceutical strategy, under a supply constraint that translates into an integral equality constraint in the control function. By applying the Pontryagin Minimum Principle, a characterization of an optimal control is provided.

q-bio.PE↗

arXiv2026

Optimizing vaccine allocation in an age-structured SIR model

We study an optimal control problem where the objective is to find the best vaccine allocation during an epidemic outbreak. The epidemic dynamics is described by an age-structured SIR model with nonlocal interactions. Both the infection and death rates depend on the age of the individuals, reflecting the effect of heterogeneities within the population. Our model includes a vaccination term, depending on time and age, which serves as a control function. The aim is to minimize the impact of the epidemic, that is, the number of casualties, under the constraint of limited vaccine supply. In a first part, we show that our optimization problem is equivalent to another static optimization problem. We then use this new optimization problem to obtain qualitative properties for the optimal allocations of vaccines.

math.OC↗

arXiv2023

Modelling coevolutionary dynamics in heterogeneous SI epidemiological systems across scales

We develop a new structured compartmental model for the coevolutionary dynamics between susceptible and infectious individuals in heterogeneous SI epidemiological systems. In this model, the susceptible compartment is structured by a continuous variable that represents the level of resistance to infection of susceptible individuals, while the infectious compartment is structured by a continuous variable that represents the viral load of infectious individuals. We first formulate an individual-based model wherein the dynamics of single individuals is described through stochastic processes, which permits a fine-grain representation of individual dynamics and captures stochastic variability in evolutionary trajectories amongst individuals. Next we formally derive the mesoscopic counterpart of this model, which consists of a system of coupled integro-differential equations for the population density functions of susceptible and infectious individuals. Then we consider an appropriately rescaled version of this system and we carry out formal asymptotic analysis to derive the corresponding macroscopic model, which comprises a system of coupled ordinary differential equations for the proportions of susceptible and infectious individuals, the mean level of resistance to infection of susceptible individuals, and the mean viral load of infectious individuals. Overall, this leads to a coherent mathematical representation of the coevolutionary dynamics between susceptible and infectious individuals across scales. We provide well-posedness results for the mesoscopic and macroscopic models, and we show that there is excellent agreement between analytical results on the long-time behaviour of the components of the solution to the macroscopic model, the results of Monte Carlo simulations of the individual-based model, and numerical solutions of the macroscopic model.

q-bio.PE↗