Liyanage Yuganthi R, Chowell Gerardo, Pogudin Gleb, Tuncer Necibe
Department of Mathematics and Statistics, Florida Atlantic University, Boca Raton, FL 33431, USA.
School of Public Health, Georgia State University, Atlanta, GA 30303, USA.
Viruses. 2025 Mar 29;17(4):496. doi: 10.3390/v17040496.
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 package in JULIA. We validated the structural identifiability results by performing parameter estimation and forecasting using the 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 assessed 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.
现象学模型是利用现实世界数据预测疾病动态的高效工具，特别是在疾病机制详细知识有限的情况下。然而，它们的可靠性取决于模型参数的结构可识别性和实际可识别性。在本研究中，我们系统地分析了流行病学中六种常用增长模型的可识别性：广义增长模型（GGM）、广义逻辑模型（GLM）、理查兹模型、广义理查兹模型（GRM）、冈珀茨模型以及具有非均匀混合的修正SEIR模型。为应对这些模型中非整数幂指数带来的挑战，我们通过引入额外的状态变量对其进行重新表述。这使得能够使用JULIA中的包进行严格的结构可识别性分析。我们使用MATLAB工具箱进行参数估计和预测，从而验证结构可识别性结果。该工具箱旨在基于现象学增长模型拟合和预测时间序列轨迹。我们将其应用于三个流行病学数据集：猴痘、新冠病毒病和埃博拉的每周发病率数据。此外，我们通过蒙特卡罗模拟评估实际可识别性，以评估在不同观测噪声水平下参数估计的稳健性。我们的结果证实，在所提出的重新表述下，所有六个模型在结构上都是可识别的。此外，实际可识别性分析表明，尽管不同模型和数据集的敏感性有所不同，但参数估计在不同噪声水平下仍保持稳健。这些发现为现象学模型描述疫情轨迹的优势和局限性提供了关键见解，强调了它们对现实世界挑战的适应性及其在为公共卫生干预提供信息方面的作用。
