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

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.