Heterogeneously structured compartmental models of epidemiological systems: from individual-level processes to population-scale dynamics
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909734603325440 |
|---|---|
| author | Bernardi, Emanuele Lorenzi, Tommaso Sensi, Mattia Tosin, Andrea |
| author_facet | Bernardi, Emanuele Lorenzi, Tommaso Sensi, Mattia Tosin, Andrea |
| contents | We develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based model that describes the dynamics of single individuals in terms of stochastic processes. Then we formally derive: (i) the mesoscopic counterpart of this model, which is formulated as a system of integro-differential equations for the distributions of individuals over the structuring-variable domains of the different compartments; (ii) the corresponding macroscopic model, which takes the form of a system of ordinary differential equations for the fractions of individuals in the different compartments and the mean levels of expression of the traits represented by the structuring variables. We employ a reduced version of the macroscopic model to obtain a general formula for the basic reproduction number, $\mathcal{R}_0$, in terms of key parameters and functions of the underlying microscopic model, so as to illustrate how such a modelling framework makes it possible to draw connections between fundamental individual-level processes and population-scale dynamics. Finally we apply the modelling framework to case studies based on classical compartmental epidemiological systems, for each of which we report on Monte Carlo simulations of the individual-based model as well as on analytical results and numerical solutions of the macroscopic model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heterogeneously structured compartmental models of epidemiological systems: from individual-level processes to population-scale dynamics Bernardi, Emanuele Lorenzi, Tommaso Sensi, Mattia Tosin, Andrea Populations and Evolution Dynamical Systems We develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based model that describes the dynamics of single individuals in terms of stochastic processes. Then we formally derive: (i) the mesoscopic counterpart of this model, which is formulated as a system of integro-differential equations for the distributions of individuals over the structuring-variable domains of the different compartments; (ii) the corresponding macroscopic model, which takes the form of a system of ordinary differential equations for the fractions of individuals in the different compartments and the mean levels of expression of the traits represented by the structuring variables. We employ a reduced version of the macroscopic model to obtain a general formula for the basic reproduction number, $\mathcal{R}_0$, in terms of key parameters and functions of the underlying microscopic model, so as to illustrate how such a modelling framework makes it possible to draw connections between fundamental individual-level processes and population-scale dynamics. Finally we apply the modelling framework to case studies based on classical compartmental epidemiological systems, for each of which we report on Monte Carlo simulations of the individual-based model as well as on analytical results and numerical solutions of the macroscopic model. |
| title | Heterogeneously structured compartmental models of epidemiological systems: from individual-level processes to population-scale dynamics |
| topic | Populations and Evolution Dynamical Systems |
| url | https://arxiv.org/abs/2503.11225 |