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A dynamically-consistent nonstandard finite difference scheme for the SICA model. 2021

Sandra Vaz, and Delfim F M Torres
Center of Mathematics and Applications (CMA-UBI), Department of Mathematics, University of Beira Interior, Covilhã 6201-001, Portugal.

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.

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