A novel sub-epidemic modeling framework for short-term forecasting epidemic waves

Abstract

Background Simple phenomenological growth models can be useful for estimating transmission parameters and forecasting epidemic trajectories. However, most existing phenomenological growth models only support single-peak outbreak dynamics whereas real epidemics often display more complex transmission trajectories. Methods We develop and apply a novel sub-epidemic modeling framework that supports a diversity of epidemic trajectories including stable incidence patterns with sustained or damped oscillations to better understand and forecast epidemic outbreaks. We describe how to forecast an epidemic based on the premise that the observed coarse-scale incidence can be decomposed into overlapping sub - epidemics at finer scales. We evaluate our modeling framework using three outbreak datasets: Severe Acute Respiratory Syndrome (SARS) in Singapore, plague in Madagascar, and the ongoing Ebola outbreak in the Democratic Republic of Congo (DRC) and four performance metrics. Results The sub-epidemic wave model outperforms simpler growth models in short-term forecasts based on performance metrics that account for the uncertainty of the predictions namely the mean interval score (MIS) and the coverage of the 95% prediction interval. For example, we demonstrate how the sub-epidemic wave model successfully captures the 2-peak pattern of the SARS outbreak in Singapore. Moreover, in short-term sequential forecasts, the sub-epidemic model was able to forecast the second surge in case incidence for this outbreak, which was not possible using the simple growth models. Furthermore, our findings support the view that the national incidence curve of the Ebola epidemic in DRC follows a stable incidence pattern with periodic behavior that can be decomposed into overlapping sub-epidemics. Conclusions Our findings highlight how overlapping sub-epidemics can capture complex epidemic dynamics, including oscillatory behavior in the trajectory of the epidemic wave. This observation has significant implications for interpreting apparent noise in incidence data where the oscillations could be dismissed as a result of overdispersion, rather than an intrinsic part of the epidemic dynamics. Unless the oscillations are appropriately modeled, they could also give a false positive, or negative, impression of the impact from public health interventions. These preliminary results using sub-epidemic models can help guide future efforts to better understand the heterogenous spatial and social factors shaping sub-epidemic patterns for other infectious diseases. Electronic supplementary material The online version of this article (10.1186/s12916-019-1406-6) contains supplementary material, which is available to authorized users.

Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020

“…We generate short-term forecasts in real-time using three phenomenological models that have been previously used to derive short-term forecasts for a number of epidemics for several infectious diseases, including SARS, Ebola, pandemic influenza, and dengue (Chowell, Tariq, & Hyman, 2019;Pell et al, 2018;Wang, Wu, & Yang, 2012). The generalized logistic growth model (GLM) extends the simple logistic growth model to accommodate sub-exponential growth dynamics with a scaling of growth parameter, p (Viboud, Simonsen, & Chowell, 2016).…”

Short-term Forecasts of the COVID-19 Epidemic in Guangdong and Zhejiang, China: February 13–23, 2020

“…We use three phenomenological models that have been previously applied to various infectious disease outbreaks including other respiratory illnesses, such as severe acute respiratory syndrome (SARS) and pandemic influenza [10,11], and to this current outbreak [12]. The generalized logistic growth model (GLM) and the Richards model extend the simple logistic growth model with an additional scaling parameter [9,11,13].…”

“…The generalized logistic growth model (GLM) and the Richards model extend the simple logistic growth model with an additional scaling parameter [9,11,13]. We also apply a sub-epidemic model, which accommodates complex epidemic trajectories, such as multiple peaks and sustained or damped oscillations, by assembling the contribution of inferred overlapping sub-epidemics [10]. Appendix A includes a detailed description of the models and their parameters.…”

“…While the GLM and Richards model only accommodate s-shaped dynamics, the sub-epidemic wave model supports complex epidemic trajectories by aggregating asynchronous sub-epidemics. For this approach, we assume that the observed curve is the aggregate of multiple overlapping sub-epidemics, where each sub-epidemic is modeled using the GLM [10]. An epidemic wave composed of n overlapping sub-epidemics is modeled as…”

“…. , n), K i is the size of the i th sub-epidemic, and the growth rate r and scaling parameter p are the same across sub-epidemics [10]. Further, when n = 1, the model returns to the single-equation GLM as presented above.…”