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

TL;DR

This paper develops a nonstandard finite difference scheme for the SICA model that preserves key dynamical properties like positivity, boundedness, and stability, ensuring accurate and reliable numerical simulations.

Contribution

It introduces a novel discretization method that maintains the continuous model's essential dynamical features, improving numerical analysis of the SICA model.

Findings

The scheme preserves positivity and boundedness of solutions.

It maintains the stability of equilibrium points.

The discretized model is dynamically consistent with the continuous model.

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.