GLOBAL STABILITY FOR A HIV/AIDS MODEL

J. Sılva Cristiana; M. Torres Delfım F.

doi:10.1501/Commua1_0000000833

EN

GLOBAL STABILITY FOR A HIV/AIDS MODEL

Abstract

We investigate global stability properties of a HIV/AIDS population model with constant recruitment rate, mass action incidence, and variablepopulation size. Existence and uniqueness results for disease-free and endemicequilibrium points are proved. Global stability of the equilibria is obtainedthrough Lyapunov’s direct method and LaSalle’s invariance principle

Keywords

HIV/AIDS mathematical model,global stability,Lyapunov functions

References

U. L. Abbas, R. M. Anderson and J. W. Mellors, Potential Impact of Antiretroviral Chemo- prophylaxis on HIV-1 Transmission in Resource-Limited Settings, PLoS ONE 2 (2007), e875. [2] R. M. Anderson, The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS J. AIDS 1 (1988), 241–256.
R. M. Anderson, G. F. Medley, R. M. May and A. M. Johnson, A Preliminary Study of the Transmission Dynamics of the Human Immunode…ciency Virus (HIV), the Causative Agent of AIDS, IMA J. Math. Appl. Med. and Biol. 3 (1986), 229–263.
S. M. Blower, D. Hartel, H. Dowlatabadi, R. M. Anderson and R. M. May, Drugs, Sex and HIV: A Mathematical Model for New York City, Phil. Trans. R. Soc. Lond. B 321 (1991), 171–187.
L. Cai, X. Li, M. Ghosh and B. Guo, Stability analysis of an HIV/AIDS epidemic model with treatment, Journal of Computational and Applied Mathematics 229 (2009), 313–323.
P. W. David, G. L. Matthew, E. G. Andrew, A. C. David and M. K. John, Relation between HIV viral load and infectiousness: A model-based analysis, The Lancet 372 (2008), no. 9635, 314–320.
S. G. Deeks, S. R. Lewin and D. V. Havlir, The end of AIDS: HIV infection as a chronic disease, The Lancet, 382 (2013), no. 9903, 1525–1533.
R. Denysiuk, C. J. Silva and D. F. M. Torres, Multiobjective approach to optimal control for a tuberculosis model, Optim. Methods Softw. 30 (2015), no. 5, 893–910.
H. Hai-Feng, C. Rui and W. Xun-Yang, Modelling and stability of HIV/AIDS epidemic model with treatment, Applied Mathematical Modelling 40 (2016), 6550–6559.

H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42 (2000), 599–653.
H. W. Hethcote and J. W. Van Ark, Modeling HIV Transmission and AIDS in the United States, Lecture notes in Biomathematics, Springer-Verlag, New York, 1992.
H. Huo and L. Feng, Global stability for an HIV/AIDS epidemic model with diğ erent latent stages and treatment, Applied Mathematical Modelling 37 (2013), 1480–1489.
J. M. Hyman and E. A. Stanley, Using mathematical models to understand the AIDS epi- demic, Mathematical Biosciences 90 (1988), 415–473.
V. Lakshmikantham, S. Leela and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, Inc., New York and Basel, 1989.
J. P. LaSalle, The Stability of Dynamical Systems, in: Regional Conferences Series in Applied Mathematics, SIAM, Philadelphia, 1976.
J. Li, Y. Yanga and Y. Zhoub, Global stability of an epidemic model with latent stage and vaccination Nonlinear Analysis: Real World Applications 12 (2011), 2163–2173.
Z. Mukandavire and W. Garirar, Eğ ect of Public Health Educational Campaigns and the Role of Sex Workers on the Spread of HIV/AIDS among Heterosexuals, Theoretical Population Biology 72 (2007), 346–365.
R. Naresh, A. Tripathi and S. Omar, Modelling the spread of AIDS epidemic with vertical transmission, Applied Mathematics and Computation 178 (2006), 262–272
F. Nyabadza, Z. Mukandavire and S. D. Hove-Musekwa, Modelling the HIV/AIDS epidemic trends in South Africa: Insights from a simple mathematical model, Nonlinear Anal. Real World Appl. 12 (2011), 2091–2104.
A. Rachah and D. F. M. Torres, Mathematical modelling, simulation, and optimal control of the 2014 Ebola outbreak in West Africa, Discrete Dyn. Nat. Soc. 2015 (2015), Art. ID 842792, 9 pp.
H. S. Rodrigues, M. T. T. Monteiro and D. F. M. Torres, Vaccination models and optimal control strategies to dengue, Math. Biosci. 247 (2014), 1–12.
A. Sani, D. P. Kroese and P. K. Pollet, Stochastic Models for the Spread of HIV in a Mobile Heterosexual Population, Math Biosc 208 (2007), 98–124.
D. Sharma, Modelling and analysis of the spread of AIDS epidemic with immigration of HIV infectives, Mathematical and Computer Modelling 49 (2009), 880–892.
C. J. Silva and D. F. M. Torres, A TB-HIV/AIDS coinfection model and optimal control treatment, Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639–4663.
A. Tripathi, R. Naresh and D. Sharma, Modelling the eğ ect of screening of unaware infectives on the spread of HIV infection, Applied Mathematics and Computation 184 (2007), 1053– 1068.

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Primary Language

English

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Authors

J. Sılva Cristiana This is me

M. Torres Delfım F. This is me

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February 1, 2018

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Year 2018 Volume: 67 Number: 1

DOI

https://doi.org/10.1501/Commua1_0000000833

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https://izlik.org/JA32EN47KB

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APA

Sılva Cristiana, J., & Torres Delfım F., M. (2018). GLOBAL STABILITY FOR A HIV/AIDS MODEL. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 93-101. https://doi.org/10.1501/Commua1_0000000833

AMA

1.Sılva Cristiana J, Torres Delfım F. M. GLOBAL STABILITY FOR A HIV/AIDS MODEL. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):93-101. doi:10.1501/Commua1_0000000833

Chicago

Sılva Cristiana, J., and M. Torres Delfım F. 2018. “GLOBAL STABILITY FOR A HIV AIDS MODEL”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 (1): 93-101. https://doi.org/10.1501/Commua1_0000000833.

EndNote

Sılva Cristiana J, Torres Delfım F. M (February 1, 2018) GLOBAL STABILITY FOR A HIV/AIDS MODEL. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 93–101.

IEEE

[1]J. Sılva Cristiana and M. Torres Delfım F., “GLOBAL STABILITY FOR A HIV/AIDS MODEL”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67, no. 1, pp. 93–101, Feb. 2018, doi: 10.1501/Commua1_0000000833.

ISNAD

Sılva Cristiana, J. - Torres Delfım F., M. “GLOBAL STABILITY FOR A HIV AIDS MODEL”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (February 1, 2018): 93-101. https://doi.org/10.1501/Commua1_0000000833.

JAMA

1.Sılva Cristiana J, Torres Delfım F. M. GLOBAL STABILITY FOR A HIV/AIDS MODEL. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:93–101.

MLA

Sılva Cristiana, J., and M. Torres Delfım F. “GLOBAL STABILITY FOR A HIV AIDS MODEL”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 67, no. 1, Feb. 2018, pp. 93-101, doi:10.1501/Commua1_0000000833.

Vancouver

1.J. Sılva Cristiana, M. Torres Delfım F. GLOBAL STABILITY FOR A HIV/AIDS MODEL. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018 Feb. 1;67(1):93-101. doi:10.1501/Commua1_0000000833

On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative

Journal of Inequalities and Applications

https://doi.org/10.1186/s13660-024-03098-1

Impact of Awareness and Protective Measures on the Transmission Dynamics of HIV/AIDS: A Mathematical Analysis

International Journal of Applied and Computational Mathematics

https://doi.org/10.1007/s40819-025-01911-z

GLOBAL STABILITY FOR A HIV/AIDS MODEL

GLOBAL STABILITY FOR A HIV/AIDS MODEL

Abstract

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Abstract

References

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Cited By

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Analysis of HIV/AIDS model with Mittag-Leffler kernel

Optimal control of an HIV model with a trilinear antibody growth function

A qualitative analysis of aMycoplasma genitaliumepidemiological model

Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel

Analysis of global stability of HIV/AIDS epidemic model in homogeneous community

Stability of a fractional HIV/AIDS model

On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative

Impact of Awareness and Protective Measures on the Transmission Dynamics of HIV/AIDS: A Mathematical Analysis