American Journal of Applied Mathematics

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A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia

Received: 22 April 2020    Accepted: 15 May 2020    Published: 29 May 2020
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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.

DOI 10.11648/j.ajam.20200803.16
Published in American Journal of Applied Mathematics (Volume 8, Issue 3, June 2020)
Page(s) 145-157
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Age Structure, HIV/AIDS Dynamics, Stability Analysis, Sensitivity Analysis, Numerical Simulation

References
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[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.
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[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.
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[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.
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Author Information
  • Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia

  • Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia

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    Tibebu Tulu Guya, Temesgen Tibebu Mekonnen. (2020). A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia. American Journal of Applied Mathematics, 8(3), 145-157. https://doi.org/10.11648/j.ajam.20200803.16

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    Tibebu Tulu Guya; Temesgen Tibebu Mekonnen. A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia. Am. J. Appl. Math. 2020, 8(3), 145-157. doi: 10.11648/j.ajam.20200803.16

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    AMA Style

    Tibebu Tulu Guya, Temesgen Tibebu Mekonnen. A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia. Am J Appl Math. 2020;8(3):145-157. doi: 10.11648/j.ajam.20200803.16

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  • @article{10.11648/j.ajam.20200803.16,
      author = {Tibebu Tulu Guya and Temesgen Tibebu Mekonnen},
      title = {A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia},
      journal = {American Journal of Applied Mathematics},
      volume = {8},
      number = {3},
      pages = {145-157},
      doi = {10.11648/j.ajam.20200803.16},
      url = {https://doi.org/10.11648/j.ajam.20200803.16},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20200803.16},
      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.},
     year = {2020}
    }
    

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    T1  - A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia
    AU  - Tibebu Tulu Guya
    AU  - Temesgen Tibebu Mekonnen
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    JO  - American Journal of Applied Mathematics
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    AB  - 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.
    VL  - 8
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