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Summary

This study analyzes a diffusive diarrhea epidemic model, revealing its stability and the role of the basic reproductive number (R0) in disease dynamics. Numerical methods confirm the model

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Infectious Disease Modeling

Background:

  • Diarrhea remains a significant global health concern.
  • Classical epidemic models often lack spatial dynamics.
  • Understanding disease spread requires robust mathematical frameworks.

Purpose of the Study:

  • To analyze the dynamics of a diffusive diarrhea epidemic model.
  • To incorporate spatial diffusion into a classical diarrhea model.
  • To investigate the model's stability and numerical solutions.

Main Methods:

  • Development of a diffusive diarrhea epidemic model with diffusion terms.
  • Analytical investigation of steady states (disease-free and endemic).
  • Design and analysis of an implicit nonstandard finite difference scheme for numerical solutions.

Main Results:

  • The model exhibits two steady states: disease-free and endemic equilibrium.
  • Analytical results confirm positivity, boundedness, and stability of steady states.
  • Numerical simulations demonstrate the scheme's positivity, boundedness, convergence, and the influence of R0.

Conclusions:

  • The diffusive model provides insights into diarrhea spread dynamics.
  • The developed numerical scheme is reliable and effective for the model.
  • The basic reproductive number (R0) is crucial for disease persistence.