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

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

Sandra Vaz  1 , Delfim F M Torres  2
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Free article

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

Sandra Vaz et al. Math Biosci Eng. .
Free article

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.

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