Simple epidemic models with segmentation can be better than complex ones

Abstract

Given a sequence of epidemic events, can a single epidemic model capture its dynamics during the entire period? How should we divide the sequence into segments to better capture the dynamics? Throughout human history, infectious diseases (e.g., the Black Death and COVID-19) have been serious threats. Consequently, understanding and forecasting the evolving patterns of epidemic events are critical for prevention and decision making. To this end, epidemic models based on ordinary differential equations (ODEs), which effectively describe dynamic systems in many fields, have been employed. However, a single epidemic model is not enough to capture long-term dynamics of epidemic events especially when the dynamics heavily depend on external factors (e.g., lockdown and the capability to perform tests). In this work, we demonstrate that properly dividing the event sequence regarding COVID-19 (specifically, the numbers of active cases, recoveries, and deaths) into multiple segments and fitting a simple epidemic model to each segment leads to a better fit with fewer parameters than fitting a complex model to the entire sequence. Moreover, we propose a methodology for balancing the number of segments and the complexity of epidemic models, based on the Minimum Description Length principle. Our methodology is (a) Automatic: not requiring any user-defined parameters, (b) Model-agnostic: applicable to any ODE-based epidemic models, and (c) Effective: effectively describing and forecasting the spread of COVID-19 in 70 countries.