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.

A class forecasting method for time series

“…Furthermore, in order to describe the complexity of each series, a second-order polynomial is fit and the coefficient of correlation, 𝑅 2 is reported. The rationale for this characterization is that time series with complex behavior will correspond to lower values of 𝑅 2 . Table 1 shows the comparative results using the number of correct forecasts based on the 𝑀 − 𝐿 = 20 − 3 = 17 time periods in the training matrix.…”

“…The large body of literature in this discipline shows how advanced as well as how elusive its main goal remains. Excellent forecasting reviews are easy to find, for example [1], however, looking at the diversity of tools available it is interesting to note that methods that are simple, transparent and effective are well sought after [2)] [ 3]. This is true even when machine learning and artificial intelligence methods have gained a lot of ground as forecasting tools [4] [5].…”

A Mathematical Study for the Transmission of Coronavirus Disease

“…Additionally, it aids in choosing the most appropriate preventive strategies to use. Several epidemic models have been presented [4][5][6][7][8][9] and the references therein to comprehend and forecast the spread of infectious diseases. The susceptible and infectious populations are separated into two categories in the SI model, and the size of each group varies according to predetermined differential equations.…”

A model for COVID-19 and bacterial pneumonia coinfection with community- and hospital-acquired infections

“…However, the complexity of these methods often precludes an intuitive understanding of the interactions between its variables and parameters [19], and simple models that can be adequately fitted to some epidemic data can be more useful than more complex models that also provide an adequate fit to the same data [20]. Deterministic ODE models have the advantage of having an extensive theory for their theoretical and numerical study [21], they have also been successfully fitted to real-world epidemic data and their prediction accuracy can be improved by methods such as segmentation of epidemic event sequences [22].…”