EPITIME: A Computational Framework for Integral Epidemic Models with Structure-Preserving Discretizations

Bruno Buonomo^1,*, Eleonora Messina¹, Claudia Panico¹, Mario Pezzella², Gaetano Zanghirati³
1 Department of Mathematics and Applications “Renato Caccioppoli”, University of Naples Federico II, Via Cintia, Naples, Italy
2 Institute for Applied Mathematics “Mauro Picone”, National Research Council of Italy, Via P. Castellino, Naples, Italy
3 Department of Mathematics and Computer Science, University of Ferrara, Via Saragat, Ferrara, Italy
* Corresponding Author: Bruno Buonomo. Email: email
(This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2026.084828

Received 29 April 2026; Accepted 30 July 2026; Published online 04 September 2026

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Abstract

EPITIME, a computational framework for the simulation of two classes of integral epidemic models, namely an age of infection model and an information-dependent behavioural model, is presented. The main contributions of this work are the design and implementation of a modular MATLAB/Python software environment built upon previously developed structure-preserving non-standard finite difference discretizations. The solvers are complemented by input parsing and validation routines, performance indicators, reproducibility tools and user-oriented graphical interfaces. The preserved structures are specific to the underlying model and include positivity, monotonicity, final-size behaviour and extinction of infectivity for the age of infection model, and positivity, boundedness, positively invariant regions and equilibrium/threshold structure for the behavioural model. The numerical schemes for both model classes and their main analytical properties, including first-order convergence, are outlined. The software architecture is then described and its use is illustrated through numerical experiments on asymptotic behaviour, inverse reconstruction of an infectivity kernel from COVID-19 incidence data, and behavioural dynamics under different memory kernels. Performance, scalability and computational complexity analyses, together with comparisons against quadrature-based approaches, are also presented. Overall, EPITIME provides a reliable and accessible computational environment for the numerical study of renewal epidemic models.