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

Sandra Vaz; Delfim F. M. Torres; Sandra Vaz; Delfim F. M. Torres

doi:10.3934/mbe.2021231

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 4552-4571. doi: 10.3934/mbe.2021231

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

Sandra Vaz ^{1
,
,},
Delfim F. M. Torres ²

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

Received: 23 March 2021 Accepted: 20 May 2021 Published: 26 May 2021

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.
- SICA model,
- compartmental models,
- stability analysis,
- Schur–Cohn criterion,
- Lyapunov functions,
- discretization by Mickens method
Citation: Sandra Vaz, Delfim F. M. Torres. A dynamically-consistent nonstandard finite difference scheme for the SICA model[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 4552-4571. doi: 10.3934/mbe.2021231

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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.

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