Specification testing for ordinary differential equation models with fixed design and applications to COVID-19...

Area of Science:

• Epidemiology
• Mathematical Biology
• Statistics

Background:

• Accurate modeling of the Coronavirus Disease 2019 (COVID-19) pandemic is crucial for understanding and predicting disease spread.
• Ordinary Differential Equation (ODE) models, like SIR and SEIR, are commonly used but often face limitations due to partially observed data.
• Existing methods may not adequately validate these models when data is incomplete.

Purpose of the Study:

• To develop and present a novel statistical test for evaluating partially observed Ordinary Differential Equation (ODE) models.
• To investigate the asymptotic properties of this test under various hypotheses.
• To assess the applicability of the SEIR model for COVID-19 data using the proposed test.

Main Methods:

• A new statistical test designed for partially observed ODE models with a fixed sampling scheme was developed.
• The test's asymptotic properties were analyzed under null, global, and local alternative hypotheses.
• Two new propositions concerning U-statistics with varying kernels for independent, non-identical data were derived as theoretical tools.
• Simulation studies were conducted to evaluate the test's performance.

Main Results:

• The proposed test demonstrates asymptotic properties under different hypotheses, providing a robust framework for model evaluation.
• Simulation studies confirmed the test's effectiveness in performance examination.
• Application to public COVID-19 data indicated that the SEIR model might be inappropriate for modeling infective cases in Japan and Algeria during specific periods.

Conclusions:

• The developed statistical test offers a valuable tool for validating ODE models, especially when dealing with partially observed epidemic data.
• The findings suggest caution in applying the SEIR model to specific COVID-19 datasets from Japan and Algeria, highlighting the need for rigorous model checking.
• This research contributes to the statistical methodology for analyzing epidemic models in public health surveillance.