Measuring differences between phenomenological growth models applied to epidemiology

Structural and Practical Identifiability of Phenomenological Growth Models for Epidemic Forecasting

Phenomenological models are highly effective tools for forecasting disease dynamics using real-world data, particularly in scenarios where detailed knowledge of disease mechanisms is limited. However, their reliability depends on the model parameters' structural and practical identifiability. In this study, we systematically analyze the identifiability of six commonly used growth models in epidemiology: the generalized growth model (GGM), the generalized logistic model (GLM), the Richards model, the generalized Richards model (GRM), the Gompertz model, and a modified SEIR model with inhomogeneous mixing. To address challenges posed by non-integer power exponents in these models, we reformulate them by introducing additional state variables. This enables rigorous structural identifiability analysis using the StructuralIdentifiability.jl package in JULIA. We validate the structural identifiability results by performing parameter estimation and forecasting using the GrowthPredict MATLAB toolbox. This toolbox is designed to fit and forecast time-series trajectories based on phenomenological growth models. We applied it to three epidemiological datasets: weekly incidence data for monkeypox, COVID-19, and Ebola. Additionally, we assess practical identifiability through Monte Carlo simulations to evaluate parameter estimation robustness under varying levels of observational noise. Our results confirm that all six models are structurally identifiable under the proposed reformulation. Furthermore, practical identifiability analyses demonstrate that parameter estimates remain robust across different noise levels, though sensitivity varies by model and dataset. These findings provide critical insights into the strengths and limitations of phenomenological models to characterize epidemic trajectories, emphasizing their adaptability to real-world challenges and their role in informing public health interventions.

Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach

Traditional compartmental models of epidemic transmission often predict an initial phase of exponential growth, assuming uniform susceptibility and interaction within the population. However, empirical outbreak data frequently show early stages of sub-exponential growth in case incidences, challenging these assumptions and indicating that traditional models may not fully encompass the complexity of epidemic dynamics. This discrepancy has been addressed through models that incorporate early behavioral changes or spatial constraints within contact networks. In this paper, we propose the concept of "frailty", which represents the variability in individual susceptibility and transmission, as a more accurate approach to understanding epidemic growth. This concept shifts our understanding from a purely exponential model to a more nuanced, generalized model, depending on the level of heterogeneity captured by the frailty parameter. By incorporating this type of heterogeneity, often overlooked in traditional models, we present a novel mathematical framework. This framework enhances our understanding of how individual differences affect key epidemic metrics, including reproduction numbers, epidemic size, likelihood of stochastic extinction, impact of public health interventions, and accuracy of disease forecasts. By accounting for individual heterogeneity, our approach suggests that a more complex and detailed understanding of disease spread is necessary to accurately predict and manage outbreaks.

Country-report pattern corrections of new cases allow accurate 2-week predictions of COVID-19 evolution with the Gompertz model

Accurate short-term predictions of COVID-19 cases with empirical models allow Health Officials to prepare for hospital contingencies in a two-three week window given the delay between case reporting and the admission of patients in a hospital. We investigate the ability of Gompertz-type empiric models to provide accurate prediction up to two and three weeks to give a large window of preparation in case of a surge in virus transmission. We investigate the stability of the prediction and its accuracy using bi-weekly predictions during the last trimester of 2020 and 2021. Using data from 2020, we show that understanding and correcting for the daily reporting structure of cases in the different countries is key to accomplish accurate predictions. Furthermore, we found that filtering out predictions that are highly unstable to changes in the parameters of the model, which are roughly 20%, reduces strongly the number of predictions that are way-off. The method is then tested for robustness with data from 2021. We found that, for this data, only 1-2% of the one-week predictions were off by more than 50%. This increased to 3% for two-week predictions, and only for three-week predictions it reached 10%.

A computational approach to identifiability analysis for a model of the propagation and control of COVID-19 in Chile

A computational approach is adapted to analyze the parameter identifiability of a compartmental model. The model is intended to describe the progression of the COVID-19 pandemic in Chile during the initial phase in early 2020 when government declared quarantine measures. The computational approach to analyze the structural and practical identifiability is applied in two parts, one for synthetic data and another for some Chilean regional data. The first part defines the identifiable parameter sets when these recover the true parameters used to create the synthetic data. The second part compares the results derived from synthetic data, estimating the identifiable parameter sets from regional Chilean epidemic data. Experiments provide evidence of the loss of identifiability if some initial conditions are estimated, the period of time used to fit is before the peak, and if a significant proportion of the population is involved in quarantine periods.

An Easy-to-Use Public Health-Driven Method (the Generalized Logistic Differential Equation Model) Accurately Simulated COVID-19 Epidemic in Wuhan and Correctly Determined the Early Warning Time

Introduction

Modeling on infectious diseases is significant to facilitate public health policymaking. There are two main mathematical methods that can be used for the simulation of the epidemic and prediction of optimal early warning timing: the logistic differential equation (LDE) model and the more complex generalized logistic differential equation (GLDE) model. This study aimed to compare and analyze these two models.

Methods

We collected data on (coronavirus disease 2019) COVID-19 and four other infectious diseases and classified the data into four categories: different transmission routes, different epidemic intensities, different time scales, and different regions, using R2 to compare and analyze the goodness-of-fit of LDE and GLDE models.

Results

Both models fitted the epidemic curves well, and all results were statistically significant. The R2 test value of COVID-19 was 0.924 (p < 0.001) fitted by the GLDE model and 0.916 (p < 0.001) fitted by the LDE model. The R2 test value varied between 0.793 and 0.966 fitted by the GLDE model and varied between 0.594 and 0.922 fitted by the LDE model for diseases with different transmission routes. The R2 test values varied between 0.853 and 0.939 fitted by the GLDE model and varied from 0.687 to 0.769 fitted by the LDE model for diseases with different prevalence intensities. The R2 test value varied between 0.706 and 0.917 fitted by the GLDE model and varied between 0.410 and 0.898 fitted by the LDE model for diseases with different time scales. The GLDE model also performed better with nation-level data with the R2 test values between 0.897 and 0.970 vs. 0.731 and 0.953 that fitted by the LDE model. Both models could characterize the patterns of the epidemics well and calculate the acceleration weeks.

Conclusion

The GLDE model provides more accurate goodness-of-fit to the data than the LDE model. The GLDE model is able to handle asymmetric data by introducing shape parameters that allow it to fit data with various distributions. The LDE model provides an earlier epidemic acceleration week than the GLDE model. We conclude that the GLDE model is more advantageous in asymmetric infectious disease data simulation.

An investigation of spatial-temporal patterns and predictions of the coronavirus 2019 pandemic in Colombia, 2020-2021

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 5,002,387 cases and 127,258 deaths as of October 31, 2021. The aggressive transmission dynamics of SARS-CoV-2 motivate an investigation of COVID-19 at the national and regional levels in Colombia. We utilize the case incidence and mortality data to estimate the transmission potential and generate short-term forecasts of the COVID-19 pandemic to inform the public health policies using previously validated mathematical models. The analysis is augmented by the examination of geographic heterogeneity of COVID-19 at the departmental level along with the investigation of mobility and social media trends. Overall, the national and regional reproduction numbers show sustained disease transmission during the early phase of the pandemic, exhibiting sub-exponential growth dynamics. Whereas the most recent estimates of reproduction number indicate disease containment, with Rt<1.0 as of October 31, 2021. On the forecasting front, the sub-epidemic model performs best at capturing the 30-day ahead COVID-19 trajectory compared to the Richards and generalized logistic growth model. Nevertheless, the spatial variability in the incidence rate patterns across different departments can be grouped into four distinct clusters. As the case incidence surged in July 2020, an increase in mobility patterns was also observed. On the contrary, a spike in the number of tweets indicating the stay-at-home orders was observed in November 2020 when the case incidence had already plateaued, indicating the pandemic fatigue in the country.

Bertalanffy-Pütter models for avian growth

This paper explores the ratio of the mass in the inflection point over asymptotic mass for 81 nestlings of blue tits and great tits from an urban parkland in Warsaw, Poland (growth data from literature). We computed the ratios using the Bertalanffy-Pütter model, because this model was more flexible with respect to the ratios than the traditional models. For them, there were a-priori restrictions on the possible range of the ratios. (Further, as the Bertalanffy-Pütter model generalizes the traditional models, its fit to the data was necessarily better.) For six birds there was no inflection point (we set the ratio to 0), for 19 birds the ratio was between 0 and 0.368 (lowest ratio attainable for the Richards model), for 48 birds it was above 0.5 (fixed ratio of logistic growth), and for the remaining eight birds it was in between; the maximal observed ratio was 0.835. With these ratios we were able to detect small variations in avian growth due to slight differences in the environment: Our results indicate that blue tits grew more slowly (had a lower ratio) in the presence of light pollution and modified impervious substrate, a finding that would not have been possible had we used traditional growth curve analysis.