Spread and Control of the Dynamics of HIV/AIDS-TB Co-infection in Ethiopia: A Mathematical Model Analysis

Authors

  • Yohannes Fissha Abebaw Department of Mathematics, Debre Berhan University, Debre Berhan and 445, Ethiopia
  • Temesgen Tibebu Mekonnen Department of Mathematics, Debre Berhan University, Debre Berhan and 445, Ethiopia

Keywords:

Nonlinear dynamical system, HIV/AIDS-TB co-infection, Stability Analysis, Basic Reproduction Number, Sensitive Analysis, Numerical Simulation

Abstract

In this work we considered a nonlinear deterministic dynamical system to study the dynamics of HIV/AIDS-TB co-infection in Ethiopia. We found the system exhibit disease free equilibrium point and endemic equilibrium point. For the reproduction number  the disease-free equilibrium point is locally asymptomatically stable and the endemic equilibrium point is locally asymptomatically unstable. We calculate basic reproduction number of the HIV/AIDS-TB co-infection dynamical system which depends on six parameters. Using real data collected from different sectors in Ethiopia we found that the numerical value of the basic reproduction number is. This shows that HIV/AIDS–TB co-infection spread in the society. Using sensitive analysis, we identify the most influential control parameter is the HIV/AIDS-TB co-infection transmission rate. The HIV/AIDS-TB co-infection transmission rate which numerical value to be 0.021. But the real value of is 0.74, to be 0.74 in to 0.021 by fixing the number of contacts for HIV/AIDS-TB co-infection we decrease the effective number of contacts for HIV/AIDS-TB co-infection 74 to 21.  We also perform numerical simulation based on real data collected from different health sectors in Ethiopia.  

References

. Awoke TD, Kassa SM. Optimal control strategy for TB-HIV/AIDS co-infection model in the presence of behaviour modification. Processes. 2018 May; 6(5):48.

. Bhunu CP, Garira W, Mukandavire Z. Modeling HIV/AIDS and tuberculosis coinfection. Bulletin of mathematical biology. 2009 Oct 1; 71(7):1745-80.

. Diekmann O, Heesterbeek JA, Metz JA. On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. Journal of mathematical biology. 1990 Jun; 28(4):365-82.

. Gakkhar S, Chavda N. A dynamical model for HIV–TB co-infection. Applied Mathematics and Computation. 2012 May 15; 218(18):9261-70.

. https://extranet.who.int/sree/Reports? op =Replet & name=/WHO_HQ_Reports/G2/PROD /EXT/TB Country Profile & ISO2=ET & out type=PDF

. https://www.cdc.gov/globalhivtb/where-we-work/ethiopia/ethiopia.html

. https://www.indexmundi.com/ethiopia/demographics_profile.html

. https://www.unaids.org/en/regionscountries/countries/ethiopia

. Jafaruddin, Pangaribuan RM, Ariyanto. Threshold dynamic for quasi-endemic equilibrium from co-epidemic HIV-TB model with re-infection TB in heterosexual population. In AIP Conference Proceedings 2016 Oct 24 (Vol. 1775, No. 1, p. 030041). AIP Publishing LLC.

. Jafaruddin, Sutimin, Ariyanto. A model dynamic for effect latent population to co-epidemic of HIV-TB. In AIP Conference Proceedings 2014 Feb 21 (Vol. 1587, No. 1, pp. 61-65). American Institute of Physics.

. Kelatlhegile Gosalamang Ricardo. Mathematical analysis of dual-infection: HIV and TB perspective (2016) Bio info Proteom Img Anal 2(2): 135- 139.

. Kumar, S., & Jain, S. A Mathematical Model for HIV-TB Co-infection: The Effect of Treatment. arXiv preprint arXiv: (2017). 1709.10353.

. Roeger LI, Feng Z, Castillo-Chavez C. Modeling TB and HIV co-infections. Mathematical Biosciences & Engineering. 2009 Oct 1;6(4):815.

. Long EF, Vaidya NK, Brandeau ML. Controlling co-epidemics: analysis of HIV and tuberculosis infection dynamics. Operations research. 2008 Dec; 56(6):1366-81.

. Lusiana, V., Putra, P. S., Nuraini, N., & Soewono, E. (2017, March). Mathematical modeling of transmission co-infection tuberculosis in HIV community. In AIP Conference Proceedings (Vol. 1825, No. 1, p. 020012). AIP Publishing.

. Mishra BK, Srivastava J. Mathematical model on pulmonary and multidrug-resistant tuberculosis patients with vaccination. Journal of the Egyptian mathematical Society. 2014 Jul 1; 22(2):311- 316.

. Naresh R, Sharma D, Tripathi A. Modelling the effect of tuberculosis on the spread of HIV infection in a population with density-dependent birth and death rate. Mathematical and Computer Modelling. 2009 Oct 1; 50(7-8):1154-66.

. Nthiiri JK. Mathematical modelling of tuberculosis as an opportunistic respiratory co-infection in hiv/aids in the presence of protection.

. Ozcaglar C, Shabbeer A, Vandenberg SL, Yener B, Bennett KP. Epidemiological models of Mycobacterium tuberculosis complex infections. Mathematical Biosciences. 2012 Apr 1; 236(2):77-96.

. Sharomi O, Podder CN, Gumel AB, Song B. Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment. Mathematical Biosciences & Engineering. 2008 Jan 1; 5(1):145.

. Silva CJ, Torres DF. A TB-HIV/AIDS co-infection model and optimal control treatment. arXiv preprint arXiv: 1501.03322. 2015 Jan 14.

. Sisay S, Mekonen A, Abera A, Berhan Y, Kebede T, Ferede A. An evaluation of collaboration in the TB and HIV control programme in Oromia Region, Ethiopia: Seven years of retrospective data. International Journal of Infectious Diseases. 2018 Dec 1; 77:74-81.

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Published

2021-02-05

How to Cite

Abebaw , Y. F. ., & Mekonnen , T. T. . (2021). Spread and Control of the Dynamics of HIV/AIDS-TB Co-infection in Ethiopia: A Mathematical Model Analysis. International Journal of Sciences: Basic and Applied Research (IJSBAR), 55(2), 11–34. Retrieved from https://gssrr.org/index.php/JournalOfBasicAndApplied/article/view/12253

Issue

Vol. 55 No. 2 (2021)

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Articles

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