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

Ran Liu, Lixing Zhu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

Abstract

Checking the models about the ongoing Coronavirus Disease 2019 (COVID-19) pandemic is an important issue. Some famous ordinary differential equation (ODE) models, such as the SIR and SEIR models have been used to describe and predict the epidemic trend. Still, in many cases, only part of the equations can be observed. A test is suggested to check possibly partially observed ODE models with a fixed design sampling scheme. The asymptotic properties of the test under the null, global and local alternative hypotheses are presented. Two new propositions about U-statistics with varying kernels based on independent but non-identical data are derived as essential tools. Some simulation studies are conducted to examine the performances of the test. Based on the available public data, it is found that the SEIR model, for modeling the data of COVID-19 infective cases in certain periods in Japan and Algeria, respectively, maybe not be appropriate by applying the proposed test.

Original languageEnglish
Article number107616
Number of pages20
JournalComputational Statistics and Data Analysis
Volume180
DOIs
Publication statusPublished - Apr 2023

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Local smoothing test
  • Model specification
  • Ordinary differential equations
  • SEIR model
  • U-statistics

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