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Parameter identification for a stochastic SEIRS epidemic model: case study influenza.

Anna Mummert1, Olusegun M Otunuga2

  • 1Department of Mathematics, Marshall University, One John Marshall Drive, Huntington, WV, USA.

Journal of Mathematical Biology
|May 8, 2019
PubMed
Summary

A new method identifies disease transmission rates and noise in SEIRS models. This technique accurately forecasts influenza peaks and future infection levels using US data.

Keywords:
Compartment disease modelLocal lagged adapted generalized method of momentsStochastic disease modelTime-dependent transmission rate

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Computational Statistics

Background:

  • Stochastic disease models are crucial for understanding infectious disease dynamics.
  • Accurate parameter estimation is essential for reliable disease forecasting.
  • The Susceptible-Exposed-Infectious-Temporarily Immune-Susceptible (SEIRS) model is widely used for endemic diseases.

Purpose of the Study:

  • To apply a novel parameter identification technique to a stochastic SEIRS model.
  • To estimate time-dependent disease transmission rates and noise intensity.
  • To evaluate the forecasting capabilities of the proposed method using influenza data.

Main Methods:

  • Utilized the local lagged adapted generalized method of moments (LLAGM) for parameter estimation.
  • Applied the LLAGM to a stochastic SEIRS model incorporating vital rates.
  • Validated the method using US influenza data from 2004-2005 to 2016-2017.

Main Results:

  • Successfully identified time-dependent transmission rates and noise intensity.
  • Demonstrated that transmission rate and noise interact to produce yearly infection peaks.
  • Forecasts for the 2016-2017 season and 2017 infection data showed qualitative agreement with observed trends.

Conclusions:

  • The LLAGM is a viable technique for parameter identification in stochastic epidemic models.
  • The method provides insights into the interplay of transmission dynamics and stochasticity.
  • The approach shows potential for forecasting future infectious disease levels with confidence intervals.