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

Sandra Vaz; Delfim F M Torres

doi:10.3934/mbe.2021231

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

Math Biosci Eng. 2021 May 26;18(4):4552-4571. doi: 10.3934/mbe.2021231.

Authors

Sandra Vaz¹, Delfim F M Torres²

Affiliations

¹ Center of Mathematics and Applications (CMA-UBI), Department of Mathematics, University of Beira Interior, Covilhã 6201-001, Portugal.
² Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro 3810-193, Portugal.

PMID: 34198453
DOI: 10.3934/mbe.2021231

Abstract

In this work, we derive a nonstandard finite difference scheme for the SICA (Susceptible-Infected-Chronic-AIDS) model and analyze the dynamical properties of the discretized system. We prove that the discretized model is dynamically consistent with the continuous, maintaining the essential properties of the standard SICA model, namely, the positivity and boundedness of the solutions, equilibrium points, and their local and global stability.

Keywords: Lyapunov functions; SICA model; Schur–Cohn criterion; compartmental models; discretization by Mickens method; stability analysis.

Publication types

Research Support, Non-U.S. Gov't