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

Tibebu Tulu Guya; Temesgen Tibebu Mekonnen

doi:doi:10.11648/j.ajam.20200803.16

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

Tibebu Tulu Guya, Temesgen Tibebu Mekonnen

Published in American Journal of Applied Mathematics (Volume 8, Issue 3)

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.

Published in	American Journal of Applied Mathematics (Volume 8, Issue 3)
DOI	10.11648/j.ajam.20200803.16
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), 2020. Published by Science Publishing Group

Keywords

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

References

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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).
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APA Style

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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ACS 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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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://article.sciencepublishinggroup.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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TY  - JOUR
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
Y1  - 2020/05/29
PY  - 2020
N1  - https://doi.org/10.11648/j.ajam.20200803.16
DO  - 10.11648/j.ajam.20200803.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 145
EP  - 157
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20200803.16
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
IS  - 3
ER  -

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Author Information

Tibebu Tulu Guya

Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia
Temesgen Tibebu Mekonnen

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

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APA Style

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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ACS 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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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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
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
Y1  - 2020/05/29
PY  - 2020
N1  - https://doi.org/10.11648/j.ajam.20200803.16
DO  - 10.11648/j.ajam.20200803.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 145
EP  - 157
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20200803.16
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
IS  - 3
ER  -

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