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

被引：10

作者：

Vaz, Sandra ^{[1
]}

Torres, Delfim F. M. ^{[2
]}

机构：

[1] Univ Beira Interior, Ctr Math & Applicat CMA UBI, Dept Math, P-6201001 Covilha, Portugal

[2] Univ Aveiro, Ctr Res & Dev Math & Applicat CIDMA, Dept Math, P-3810193 Aveiro, Portugal

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2021年 / 18卷 / 04期

关键词：

SICA model; compartmental models; stability analysis; Schur-Cohn criterion; Lyapunov functions; discretization by Mickens method; NUMERICAL-METHODS; COINFECTION; HIV/AIDS;

D O I：

10.3934/mbe.2021231

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：4552 / 4571

页数：20

共 50 条

[41] A nonstandard finite difference scheme for a Fisher PDE having nonlinear diffusion
Mickens, RE
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (1-3) : 429 - 436
[42] A new positivity-preserving nonstandard finite difference scheme for the DWE
Mickens, RE
Jordan, PM
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2005, 21 (05) : 976 - 985
[43] Nonstandard Finite Difference Schemes for an SIR Epidemic Model
Khalsaraei, Mohammad Mehdizadeh
Shokri, Ali
Noeiaghdam, Samad
Molayi, Maryam
[J]. MATHEMATICS, 2021, 9 (23)
[44] A nonstandard finite difference scheme for a nonlinear Black-Scholes equation
Arenas, Abraham J.
Gonzalez-Parra, Gilberto
Melendez Caraballo, Blas
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2013, 57 (7-8) : 1663 - 1670
[45] An explicit nonstandard finite difference scheme for the FitzHugh-Nagumo equations
Chapwanya, M.
Jejeniwa, O. A.
Appadu, A. R.
Lubuma, J. M. -S.
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2019, 96 (10) : 1993 - 2009
[46] Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme
Khan, Ihsan Ullah
Hussain, Amjid
Li, Shuo
Shokri, Ali
[J]. FRACTAL AND FRACTIONAL, 2023, 7 (06)
[47] An Efficient Nonstandard Finite Difference Scheme for a Class of Fractional Chaotic Systems
Hajipour, Mojtaba
Jajarmi, Amin
Baleanu, Dumitru
[J]. JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2018, 13 (02):
[48] Positive and bounded nonstandard finite difference scheme for the Hodgkin–Huxley equations
A. A. Aderogba
M. Chapwanya
[J]. Japan Journal of Industrial and Applied Mathematics, 2018, 35 : 773 - 785
[49] A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction
Mickens, RE
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2003, 62 (1-2) : 117 - 124
[50] A nonstandard finite-difference scheme for the Lotka-Volterra system
Mickens, RE
[J]. APPLIED NUMERICAL MATHEMATICS, 2003, 45 (2-3) : 309 - 314

← 1 2 3 4 5 →