A methodological approach for modeling the spread of disease using geographical discrete-event spatial models

The study of infectious disease models has become increasingly important during the COVID-19 pandemic. The forecasting of disease spread using mathematical models has become a common practice by public health authorities, assisting in creating policies to combat the spread of the virus. Common approaches to the modeling of infectious diseases include compartmental differential equations and cellular automata, both of which do not describe the spatial dynamics of disease spread over unique geographical regions. We introduce a new methodology for modeling disease spread within a pandemic using geographical models. We demonstrate how geography-based Cell-Discrete-Event Systems Specification (DEVS) and the Cadmium JavaScript Object Notation (JSON) library can be used to develop geographical cellular models. We exemplify the use of these methodologies by developing different versions of a compartmental model that considers geographical-level transmission dynamics (e.g. movement restriction or population disobedience to public health guidelines), the effect of asymptomatic population, and vaccination stages with a varying immunity rate. Our approach provides an easily adaptable framework that allows rapid prototyping and modifications. In addition, it offers deterministic predictions for any number of regions simulated simultaneously and can be easily adapted to unique geographical areas. While the baseline model has been calibrated using real data from Ontario, we can update and/or add different infection profiles as soon as new information about the spread of the disease become available.