  Since the outbreak of COVID-19, an astronomical number of publications on the
pandemic dynamics appeared in the literature, of which many use the susceptible
infected removed (SIR) and susceptible exposed infected removed (SEIR) models,
or their variants, to simulate and study the spread of the coronavirus. SIR and
SEIR are continuous-time models which are a class of initial value problems
(IVPs) of ordinary differential equations (ODEs). Discrete-time models such as
regression and machine learning have also been applied to analyze COVID-19
pandemic data (e.g. predicting infection cases), but most of these methods use
simplified models involving a small number of input variables pre-selected
based on a priori knowledge, or use very complicated models (e.g. deep
learning), purely focusing on certain prediction purposes and paying little
attention to the model interpretability. There have been relatively fewer
studies focusing on the investigations of the inherent time-lagged or
time-delayed relationships e.g. between the reproduction number (R number),
infection cases, and deaths, analyzing the pandemic spread from a systems
thinking and dynamic perspective. The present study, for the first time,
proposes using systems engineering and system identification approach to build
transparent, interpretable, parsimonious and simulatable (TIPS) dynamic machine
learning models, establishing links between the R number, the infection cases
and deaths caused by COVID-19. The TIPS models are developed based on the
well-known NARMAX (Nonlinear AutoRegressive Moving Average with eXogenous
inputs) model, which can help better understand the COVID-19 pandemic dynamics.
A case study on the UK COVID-19 data is carried out, and new findings are
detailed. The proposed method and the associated new findings are useful for
better understanding the spread dynamics of the COVID-19 pandemic.
