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A dynamically consistent computational method to solve numerically a mathematical model of polio propagation with

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  • 1Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.

Computer Methods and Programs in Biomedicine
|March 2, 2022
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Summary
This summary is machine-generated.

This study models polio spread using differential equations, incorporating spatial diffusion and analyzing disease-free and endemic states. A numerical method confirms model stability and solution positivity, aiding in understanding polio transmission dynamics.

Keywords:
Basic reproductive numberDiffusive mathematical modelGlobal stability analysisNeumann stability analysisPositivity-preserving scheme

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Area of Science:

  • Mathematical epidemiology
  • Computational biology
  • Disease modeling

Background:

  • A mathematical model using ordinary differential equations describes polio propagation.
  • The model includes four population compartments: susceptible, exposed, infected, and vaccinated individuals.

Purpose of the Study:

  • To extend a compartmental polio model to include one-dimensional spatial diffusion.
  • To analytically determine disease-free and endemic equilibria and the basic reproductive number.
  • To rigorously analyze the stability of equilibrium solutions.

Main Methods:

  • Development of a partial differential equation model incorporating spatial diffusion.
  • Analytical determination of equilibria and the basic reproductive number.
  • Implementation of an implicit, linear finite-difference method for numerical approximation.

Main Results:

  • Established nonnegativity and boundedness of model solutions.
  • Rigorous stability analysis of equilibrium points.
  • Demonstrated stability and unconditional positivity preservation of the numerical method.

Conclusions:

  • The proposed numerical method is stable and provides consistent approximations.
  • The numerical model accurately preserves the positivity of solutions.
  • Computer simulations validate theoretical findings on polio transmission dynamics.