LYAPUNOV STABILITY OF MALE CIRCUMCISION MODEL IN HIV/AIDS PREVENTIONS

Authors

  • E. S. Udofia Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Akwa Ibom State, Nigeria Author
  • H. S. Thomas Author

DOI:

https://doi.org/10.60787/tnamp-19-1-16

Keywords:

Lyapunov, Circumcision, Global Stability, HIV/AIDS, Reproductive ratio

Abstract

This work examines the contribution of a non-pharmaceutical control measure, male circumcision to combat the spread of the world’s threatening infection, the HIV/AIDS. It establishes the condition for positivity and boundedness of the model, which enhance the existence and uniqueness of the solution of the model thereby making the model to be epidemiologically meaningful.The main mathematical technique used is the Lyapunov direct method which is applied successfully to two cases: when the population is not circumcised and when the population is fully circumcised, to study the global asymptotic stability of the model. It was established that the local stability of the model is guaranteed if the product of the probability of transmission by individuals and the average number of contact per unit time is less than the sum product of circumcision rate and that of the natural death of the individual in the population. That is if circumcision is encouraged in the population it greatly enhances the eradication of HIV/AIDS. When the population is circumcised the analysis showed that, the disease free equilibrium is globally asymptotically stable in Ω if Rc0 ≤ 1.

         Views | Downloads: 32 / 0

Downloads

Download data is not yet available.

References

Catherine Hankins, Mitchell Warren, Emmanuel Njeuhmeli (2016), Voluntary Medical Male Circumcision for HIV Prevention: New

Mathematical Models for Strategic Demand Creation Prioritizing Subpopulations by Age and Geography, PLoS One. 2016 December 30; 11(12): e0169499

Ekere S. Udofia, (2023), Mathematical Model of Male Circumcision in HIV/AIDS Preventions, International Journal of Innovative Science

and Research Technology, Volume 8, Issue 8, August – 2023 ISSN No: -2456-2165 www.ijisrt.com

Udofia, EkereSunday, Sampson, Marshal Imeh (2014) , Mathematical Model of the Effect of Complacency in HIV/AIDS Preventions, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 10, Issue 6 Ver. V (Nov - Dec. 2014), PP 30-33

Udofia, Ekere Sunday and Inyama, Simeon Chioma Mathematical model of Structural Strategy ( Delayed First Intercoure) in HIVAIDS

Prevention, Journal of the Nigerian Association of Mathematical Physics Volume 24 (July, 2013) pp 257-260 © J. of NAMP

Susan Cassels, Samuel J. Clark, Martina Morris(2008),Mathematical Models for HIV Transmission Dynamics Tools for Social and Behavioral Science Research J Acquir Immune Defic Syndr. 2008 Mar 1; 47(Suppl 1): S34–S39.doi: 10.1097/QAI.0b013e3181605da3

IA Agwu, SC Inyama, RA Umana, A Omame, N Ukanwoke, A Ofomata, HI Mbachu, ES Udofia, JI Uwakwe (2018) Determining the impact of variation of Harvesting Effort on the Qualitative Behaviour of a Coexistence Steady State Solution and its Stability in Prey-Predator Fishery Model, Academic Journal of Applied Mathematical Sciences Vol. 4 Issue 10 Pages 119-128, 2018

Udofia, Ekere S, and Etukudo Idorenyin A (2019) Optimal Allocation of Biscuit Ingredient in the Production Process - An Invariant Property Based Algorithm Approach, Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) DOI: 10.7176/MTM Vol.9, No.4, 2019

Udofia Ekere Sunday and Inyama Simeon Chioma (2012) Application of Optimal Control to the Epidemiology of Fowl Pox Transmission

Dynamics in Poultry Journal of Mathematics and Statistics 8 (2): 248-252

Udofia Ekere Sunda and Inyama Simeon Chioma (2011) Mathematical Modeling of the Transmission Dynamics of Fowl Pox in Poultry,

Journal of Modern Mathematics and Statistics 5 (5-6): 106-111, 2012 ISSN 1994-5388 © 2011 Medwell Journals, 2011

Udofia Ekere Sunday , Amos Amos Idungafa (2018) Mathematical Model of Bacteria-Nutrient Harvesting in A Cultured Environment,

Journal of the Nigerian Association of Mathematical Physics Volume 46 (May, 2018 Issue), pp115 –118, 2018 © J. of NAMP

Udofia, Ekere Sunday, Sampson, Marshal Imeh (2014) Mathematical Model for the Epidemiology of Fowl Pox Infection Transmission That Incorporates Discrete Delay, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 10, Issue 4 Ver. V (July - Aug. 2014), PP 08-16 www.iosrjournals.org

Udofia Ekere Sunday and Inyama Simeon Chioma (2011) Mathematical Model of the Impact of Vaccination on the Transmission Dynamics of Fowl Pox in Poultry, Journal of Modern Mathematics and Statistics 5 (5-6): 102-105, 2012 ISSN 1994-5388 © 2011 Medwell Journals

UDOFIA EKERE SUNDAY, UDOH KENNETH JUMBO AND INYAMA SIMEON CHIOMA (2016) THE IMPACT OF MEDIA COVERAGE ON THE

TRANSMISSION DYNAMICS OF FOWL POX IN POULTRY, International J. of Math. Sci. & Engg. Appls. (IJMSEA) ISSN 0973-9424, Vol. 10 No. I (April, 2016), pp. 103-114

I. J. Udom, E. S. Udofia, S. A. Nta, G. A. Usoh, E. O. Sam (2023), Prediction of Piggery Wastewater Nutrient Attenuation by Constructed

Wetland in a Humid Environment, International Journal of Innovative Science and Research Technology ISSN No:-2456-2165 Volume 8,

Issue 9, September – 2023, www.ijisrt.com

ONUOHA JOY LJEOMA, INYAMA SIMEON CHIOMA AND UDOFIA SUNDAY EKERE(2014), Mathematical Model of the Transmission Dynamics of Swine Flu with the Vaccination of Newborns, International J. of Math. Sci. & Engg. Appls. (IJMSEA) ISSN 0973-9424, Vol. 8 No. V (September, 2014), pp. 217-229

F. Brauer P. Driessche and J. Wu, Further notes on the basic reproduction number, pp. 159–176, Springer Science and Business Media,

(April 13, 2008).

P. Driessche and Z. Shua, Global stability of infectious disease models using lyapunov functions, SIAM J. APPL.MATH 73 (2013), no. 4,

–1532.

D. Okuonghae, A. Omame (2020), Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria, Chaos,

Solitons and Fractals 139 (2020) 110032 , https://doi.org/10.1016/j.chaos.2020.110032 0960-0779/© 2020 Elsevier Ltd. All rights reserved.

ONUOHA JOY LJEOMA, INYAMA SIMEON CHIOMA, UDOFIA EKERE SUNDAY AND OMAME ANDREW (2015) Mathematical Model of the

Transmission Dynamics of Swine Flu with the Vaccination of Non Newborns, International J. of Math. Sci. & Engg. Appls. (IJMSEA) ISSN 0973-9424, Vol. 9 No. I (March, 2015), pp. 1-17 www.ascent-journals.com

J.P. LaSalle, The stability of dynamical systems, SIAM, Philadelphia, (1976).

Van den Driessche P , Watmough J . Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 2002;180:29–48 .

Udofia, Ekere Sunday and Umana, Reuben Andrew (2014), Weak Solutions of Boundary Value Problems Journal of the Nigerian

Association of Mathematical Physics Volume28, No. 1, (November, 2014), pp21 – 30© J. of NAMP.

Published

2024-03-29

How to Cite

LYAPUNOV STABILITY OF MALE CIRCUMCISION MODEL IN HIV/AIDS PREVENTIONS. (2024). The Transactions of the Nigerian Association of Mathematical Physics, 19, 1-16. https://doi.org/10.60787/tnamp-19-1-16

Share

Similar Articles

1-10 of 13

You may also start an advanced similarity search for this article.