arXiv subjects

Simone De Reggi

Publications and source records attributed to Simone De Reggi.

8 recordsLinked to original sources

arXiv2025

Behavior-induced oscillations in epidemic outbreaks with distributed memory: beyond the linear chain trick using numerical methods

We considered a model for an infectious disease outbreak, when the depletion of susceptible individuals is negligible, and assumed that individuals adapt their behavior according to the information they receive about new cases. In line with the information index approach, we supposed that individuals react to past information according to a memory kernel that is continuously distributed in the past. We analyzed equilibria and their stability, with analytical results for selected cases. Thanks to the recently developed pseudospectral approximation of delay equations, we studied numerically the long-term dynamics of the model for memory kernels defined by gamma distributions with a general non-integer shape parameter, extending the analysis beyond what is allowed by the linear chain trick. In agreement with previous studies, we showed that behavior adaptation alone can cause sustained waves of infections even in an outbreak scenario, and notably in the absence of other processes like demographic turnover, seasonality, or waning immunity. Our analysis gives a more general insight into how the period and peak of epidemic waves depend on the shape of the memory kernel and how the level of minimal contact impacts the stability of the behavior-induced positive equilibrium.

q-bio.PE↗

arXiv2025

A model for mosquito-borne epidemic outbreaks with information-dependent protective behaviour

We investigate a model for a mosquito-borne epidemic in which human hosts may adopt protective behaviour against vector bites in response to information on both past and current disease prevalence. Assuming that mosquitoes can also feed on non-competent hosts (i.e.\ hosts that do not contribute to disease transmission), we first revisit existing results and show that behaviour-driven protection may either decrease or increase the basic reproduction number, depending on the interaction between behavioural response, host composition, and transmission parameters. Assuming that opinion dynamics evolves on a much faster time scale than disease transmission, we then apply Geometric Singular Perturbation Theory to effectively reduce the original two-group model to a model for a homogeneous host population. The reduced system enables a detailed investigation of the impact of information-induced behavioural changes on the transient dynamics of the epidemic, including scenarios in which protective measures lead to outbreaks with low attack rates. Our analysis shows that behavioural responses may either facilitate epidemic control or prolong disease persistence, potentially generating recurrent damped epidemic waves. Numerical simulations are provided to illustrate and support the analytical findings.

q-bio.PE↗

arXiv2025

On the numerical computation of $R_0$ in periodic environments

We propose a novel approach to approximate the basic reproduction number $R_0$ as spectral radius of the Next-Generation Operator in time-periodic population models by characterizing the latter via evolution semigroups. Once birth/infection and transition operators are identified, we discretize them via either Fourier or Chebyshev collocation methods. Then $R_0$ is obtained by solving a generalized matrix eigenvalue problem. The order of convergence of the approximating reproduction numbers to the true one is shown to depend on the regularity of the model coefficients, and spectral accuracy is proved. We validate the theoretical results by discussing applications to epidemiology, viz. a large-size multi-group epidemic model with periodic contact rates, and a vector-borne disease model with seasonal vector recruitment. We illustrate how the method facilitates implementation compared to existing approaches and how it can be easily adapted to also compute type-reproduction numbers.

math.NA↗

arXiv2024

On the convergence of the pseudospectral approximation of reproduction numbers for age-structured models

We rigorously investigate the convergence of a new numerical method, recently proposed by the authors, to approximate the reproduction numbers of a large class of age-structured population models with finite age span. The method consists in reformulating the problem on a space of absolutely continuous functions via an integral mapping. For any chosen splitting into birth and transition processes, we first define an operator that maps a generation to the next one (corresponding to the Next Generation Operator in the case of R0). Then, we approximate the infinite-dimensional operator with a matrix using pseudospectral discretization. In this paper, we prove that the spectral radius of the resulting matrix converges to the true reproduction number, and the (interpolation of the) corresponding eigenvector converges to the associated eigenfunction, with convergence order that depends on the regularity of the model coefficients. Results are confirmed experimentally and applications to epidemiology are discussed.

math.NA↗

arXiv2024

Approximating reproduction numbers: a general numerical method for age-structured models

In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.

q-bio.PE↗

arXiv2023

A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion

We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal diffusion are more challenging since the associated semigroups have no regularizing properties in the spatial variable. Nevertheless, the asymptotic stability of the null equilibrium is determined by the spectrum of the infinitesimal generator associated to the semigroup. We propose a numerical method to approximate the leading part of this spectrum by first reformulating the problem via integration of the age-state and then by discretizing the generator combining a spectral projection in space with a pseudospectral collocation in age. A rigorous convergence analysis proving spectral accuracy is provided in the case of separable model coefficients. Results are confirmed experimentally and numerical tests are presented also for the more general instance.

math.NA↗

arXiv2022

A pseudospectral method for investigating the stability of linear population models with two physiological structures

The asymptotic stability of the null equilibrium of a linear population model with two physiological structures formulated as a first-order hyperbolic PDE is determined by the spectrum of its infinitesimal generator. We propose an equivalent reformulation of the problem in the space of absolutely continuous functions in the sense of Carathéodory, so that the domain of the corresponding infinitesimal generator is defined by trivial boundary conditions. Via bivariate collocation, we discretize the reformulated operator as a finite-dimensional matrix, which can be used to approximate the spectrum of the original infinitesimal generator. Finally, we provide test examples illustrating the converging behavior of the approximated eigenvalues and eigenfunctions, and its dependence on the regularity of the model coefficients.

math.NA↗

arXiv2021

Bivariate collocation for computing $R_{0}$ in epidemic models with two structures

Structured epidemic models can be formulated as first-order hyperbolic PDEs, where the "spatial" variables represent individual traits, called structures. For models with two structures, we propose a numerical technique to approximate $R_{0}$, which measures the transmissibility of an infectious disease and, rigorously, is defined as the dominant eigenvalue of a next-generation operator. Via bivariate collocation and cubature on tensor grids, the latter is approximated with a finite-dimensional matrix, so that its dominant eigenvalue can easily be computed with standard techniques. We use test examples to investigate experimentally the behavior of the approximation: the convergence order appears to be infinite when the corresponding eigenfunction is smooth, and finite for less regular eigenfunctions. To demonstrate the effectiveness of the technique for more realistic applications, we present a new epidemic model structured by demographic age and immunity, and study the approximation of $R_{0}$ in some particular cases of interest.

math.NA↗