Abstract Mathematical models are useful in epidemiology to understand the COVID-19 contagion dynamics. Our aim is to demonstrate the effectiveness of parameter regression methods to calibrate an established epidemiological model describing COVID-19 infection rates subject to active and varying non-pharmaceutical interventions (NPIs). To do this, we assess the potential of some established chemical engineering modelling principles and practice for application to modelling of epidemiological systems. This allows us to exploit the sophisticated functionality of a commercial chemical engineering simulator capable of parameter regression with piecewise continuous integration and event and discontinuity management. Our results provide insights into the outcomes of on-going disease suppression measures, while visualisation of reported data also provides up-to-date condition monitoring of the status of the pandemic. We observe that the effective reproduction number response to NPIs is non-linear with variable response rate, magnitude and direction. Highlights Modelling COVID-19 contagion dynamics with piecewise continuous integration and event and discontinuity management Equivalence to kinetic model with time varying stoichiometry Model calibration and estimation of non-linear variation in R e Development of prototype demonstrator algorithm for estimation of R e using data with time varying NPIs