Volume 8, Issue 3, June 2020, Page: 145-157
A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia
Tibebu Tulu Guya, Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia
Temesgen Tibebu Mekonnen, Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia
Received: Apr. 22, 2020;       Accepted: May 15, 2020;       Published: May 29, 2020
DOI: 10.11648/j.ajam.20200803.16      View  259      Downloads  150
Abstract
In this work we considered a nonlinear deterministic dynamical system to study the dynamics of HIV/AIDS with age structure and different mode of transmissions in Ethiopia. We found that the diseases free equilibrium point and endemic equilibrium points exist and we perform their local stability and global stability analysis using nonlinear stability methods. We found that the basic reproduction number of the considered dynamical system depends on the considered parameters and using real data collected from different health sectors in Ethiopia we found the numerical value of the reproduction number is R_0=1.05>1. This shows that the considered disease spreads in the community. From the sensitivity index of the dynamical system we found that the most sensitive parameter is the transmission rate of unaware infective humans to aware infectiveθ. We also showed that the effect of all parameters on the basic reproduction number using numerical simulation.
Keywords
Age Structure, HIV/AIDS Dynamics, Stability Analysis, Sensitivity Analysis, Numerical Simulation
To cite this article
Tibebu Tulu Guya, Temesgen Tibebu Mekonnen, A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia, American Journal of Applied Mathematics. Vol. 8, No. 3, 2020, pp. 145-157. doi: 10.11648/j.ajam.20200803.16
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
WHO, HIV/AIDS- Global Health Observatory (GHO) data. Retrieved from. http://www.who. int/gho/hiv/en/ (2018).
[2]
https://www.unaids.org/en/regionscountries/countries/ethiopia, (January 2020).
[3]
Temesgen Debas Awoke and Semu Mitiku Kassa, “Optimal Control Strategy for TB-HIV/AIDS Co-Infection Model in the Presence of Behaviour Modification” Processes 2018, 6, 48.
[4]
R. M. Anderson, G. F. Medley, R. M. May, and A. M. Johnson, “A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS,” IMA Journal of Mathematics Applied in Medicine and Biology, vol. 3, no. 4, pp. 229–263, 1986.
[5]
N. I. Stilianakis, K. Dietz, andD. Schenzle,“Analysisofamodel for the pathogenesis of AIDS,” Mathematical Biosciences, vol. 145, no. 1, pp. 27–46, 1997.
[6]
A. Tripathi, R. Naresh, and D. Sharma, “Modelling the effect of screening of unaware infectives on the spread of HIV infection,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 1053–1068, 2007.
[7]
A. B. Gumel, P. N. Shivakumar, and B. M. Sahai, “A mathematical model for the dynamics of HIV-1 during the typical course of infection,” Nonlinear Analysis: Theory, Methods and Applications, vol. 47, no. 3, pp. 1773–1783, 2001.
[8]
B. D. Aggarwala, “On two ode models for HIV/AIDS development in Canada and a logistic seir model,” Far East Journal of Applied Mathematics, vol. 6, no. 1, pp. 25–70, 2002.
[9]
B. Flugentius, J. Y. T. Mugisha, and L. S. Luboobi, “An HIV/AIDS model with variable force of infection and its application to the epidemic in Uganda,” The American Journal of Applied Sciences, vol. 2, pp. 1274–1278, 2005.
[10]
D. Mohammed Ibrahim and B. Seidu, “Modelling the effect of irresponsible infective immigrants on the transmission dynamics of HIV/AIDS,” Advances in Applied Mathematical Biosciences, vol. 3, pp. 31–40, 2012.
[11]
J. Chin, “Current and future dimensions of the HIV/AIDS pandemic in women and children,” The Lancet, vol. 336, no. 8709, pp. 221–224, 1990.
[12]
J. T. Bertrand, K. O’Reilly, J. Denison, R. Anhang, andM. Sweat,“ Systematic review of the effectiveness of mass communication programs to change HIV/AIDS-related behaviors in developing countries,” Health Education Research, vol. 21, no. 4, pp. 567–597, 2006.
[13]
M. I. Daabo, O. D. Makinde, and B. Seidu, “Modelling the spread of HIV/AIDS epidemic in the presence of irresponsible infectives,” African Journal of Biotechnology, vol. 11, no. 51, pp. 11287–11295, 2012.
[14]
M. Coffee, M. N. Lurie, and G. P. Garnett,“Modelling the impact of migration on the HIV epidemic in South Africa,” AIDS, vol. 21, no. 3, pp. 343–350, 2007.
[15]
P. Essunger and A. S. Perelson, “Modeling HIV infection of CD4+ t-cell subpopulations,” Journal of Theoretical Biology, vol. 170, no. 4, pp. 367–391, 1994.
[16]
Tibebu Tulu Guya and Temesgen Tibebu Mekonnen, “Treatment and Inflow Infective Immigrants on the Dynamics of HIV/AIDS” IOSR Journal of Mathematics (IOSR-JM).
[17]
Diekmann O., Heesterbeek J. A and Metz J. A., on the definition and computation of R_0 in the model for infectious disease in heterogeneous population. Journal of mathematical Biology, 28 (1990), 365-382.
[18]
P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002.
[19]
The UN Refugee Agency, ETHIOPIA Refugees and Asylum-seekers as of 30 November 2016.
[20]
https://www.indexmundi.com/ethiopia/demographics_profile.html, (Dec. 13, 2019).
[21]
E. O. Omondi, R. W. Mbogo and L. S. Luboobi, Mathematical modeling of the impact of testing, treatment and control of HIV transmission in Kenya, Omondi et al., Cogent Mathematics & Statistics (2018), 5: 1475590 https://doi.org/10.1080/25742558.2018.1475590
[22]
Mulugeta, H., Dessie, G., Wagnew, F. et al. Seroprevalence and trend of human immunodeficiency virus among blood donors in Ethiopia: a systematic review and meta-analysis. BMC Infect Dis 19, 383 (2019). https://doi.org/10.1186/s12879-019-4012-5
[23]
https://www.avert.org/about-hiv-aids/symptoms-stages, (January 29, 2020)
[24]
Tunde T. Yusuf & Francis Benyah (2012) Optimal strategy for controlling the spread of HIV/AIDS disease: a case study of South Africa, Journal of Biological Dynamics, 6:2, 475-494, DOI:10.1080/17513758.2011.628700.
[25]
https://www.macrotrends.net/countries/ETH/ethiopia/death-rate, (December 2019)
[26]
Endalamaw, A., Demsie, A., Eshetie, S. et al. A systematic review and meta-analysis of vertical transmission route of HIV in Ethiopia. BMC Infect Dis 18, 283 (2018). https://doi.org/10.1186/s12879-018-3189-3.
[27]
https://knoema.com/atlas/Ethiopia/Neonatal-mortality-rate, (February 01, 2020).
Browse journals by subject