Work

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

Year: 2024

Type: article

Abstract: 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.

Source: Mathematical Biosciences & Engineering

DOI: 10.3934/mbe.2024236

Authors: Simone De Reggi, Francesca Scarabel, Rossana Vermiglio

Institutions: University of Udine, University of Leeds

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: gold

Estimated APC paid: $1,000

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per il Calcolo Scientifico