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Interval nonlinear initial-valued problem using constraint intervals: Theory and an application to the Sars-Cov-2

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  • 1Department of Mathematics, Federal University of Mato Grosso, 78075-202 Cuiabá, MT, Brazil.

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This study introduces constraint interval solutions for analyzing epidemiological models with uncertain parameters, like COVID-19. The method effectively estimates parameter ranges and visualizes pandemic behavior under interval uncertainty.

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Area of Science:

  • Mathematical modeling
  • Epidemiology
  • Computational mathematics

Background:

  • Interval uncertainty poses challenges in modeling complex systems like disease spread.
  • Traditional models often lack robust methods for handling parameter variability.
  • The Susceptible-Infected-Recovered (SIR) model is a fundamental tool in epidemiology.

Purpose of the Study:

  • To develop and apply constraint interval solutions for nonlinear differential equations.
  • To analyze the asymptotic behavior of an SIR model under interval uncertainty, specifically for COVID-19.
  • To estimate parameter intervals and visualize pandemic dynamics using real-world data.

Main Methods:

  • The theory of constraint interval solutions was applied to interval nonlinear initial value problems.
  • The SIR model with interval parameters was analyzed for asymptotic behavior.
  • Solutions were fitted to Brazilian Sars-Cov-2 pandemic data to estimate parameter intervals.
  • Simulations and graphical representations were used to visualize results.

Main Results:

  • Constraint interval solutions provide a robust framework for analyzing models with interval uncertainty.
  • The approach successfully estimated parameter intervals for the COVID-19 SIR model.
  • Visualizations effectively demonstrated the impact of interval uncertainty on pandemic behavior.

Conclusions:

  • Constraint interval solutions are efficacious for analyzing epidemiological models with parameter uncertainty.
  • The method offers a valuable tool for understanding and predicting disease dynamics in the presence of data variability.
  • This approach enhances the reliability of epidemiological modeling for public health applications.