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A dynamically-consistent nonstandard finite difference scheme for the SICA model.

Sandra Vaz1, Delfim F M Torres2

  • 1Center of Mathematics and Applications (CMA-UBI), Department of Mathematics, University of Beira Interior, Covilhã 6201-001, Portugal.

Mathematical Biosciences and Engineering : MBE
|July 2, 2021
PubMed
Summary
This summary is machine-generated.

We developed a new numerical method for the Susceptible-Infected-Chronic-AIDS (SICA) model. This finite difference scheme accurately preserves the model's key dynamical properties, ensuring reliable simulations for HIV/AIDS research.

Keywords:
Lyapunov functionsSICA modelSchur–Cohn criterioncompartmental modelsdiscretization by Mickens methodstability analysis

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Area of Science:

  • Mathematical Biology
  • Numerical Analysis
  • Epidemiology

Background:

  • The Susceptible-Infected-Chronic-AIDS (SICA) model is crucial for understanding HIV/AIDS dynamics.
  • Accurate numerical methods are essential for simulating and analyzing epidemiological models.

Purpose of the Study:

  • To derive and analyze a nonstandard finite difference scheme for the SICA model.
  • To ensure the numerical scheme preserves critical dynamical properties of the continuous SICA model.

Main Methods:

  • Development of a nonstandard finite difference discretization for the SICA model.
  • Analysis of the dynamical properties of the resulting discrete system.
  • Proof of consistency between the discrete and continuous SICA models.

Main Results:

  • The derived finite difference scheme is dynamically consistent with the continuous SICA model.
  • The scheme maintains the positivity and boundedness of solutions.
  • Equilibrium points and their local/global stability are preserved in the discretized system.

Conclusions:

  • The proposed nonstandard finite difference scheme offers a reliable numerical tool for SICA model simulations.
  • This method ensures the accurate representation of HIV/AIDS epidemiological dynamics.
  • The validated scheme supports further research in AIDS modeling and control strategies.