A MATHEMATICAL MODEL FOR TB/HIV CO-INFECTION TREATMENT AND TRANSMISSION MECHANISM

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Published: 2018-02-07

Page: 180-192


ADEBOYE AZEEZ *

Department of Statistics (Biostatistics and Epidemiology), University of Fort Hare, Alice, Eastern Cape, South Africa.

JAMES NDEGE

Department of Statistics (Biostatistics and Epidemiology), University of Fort Hare, Alice, Eastern Cape, South Africa.

RUFFIN MUTAMBAYI

Department of Statistics (Biostatistics and Epidemiology), University of Fort Hare, Alice, Eastern Cape, South Africa.

YONGSONG QIN

Department of Statistics (Biostatistics and Epidemiology), University of Fort Hare, Alice, Eastern Cape, South Africa.

*Author to whom correspondence should be addressed.


Abstract

A Mathematical model that focuses on the underlying transmission mechanism of TB and HIV co-infection is developed and analysed to help understand and predict the spread and progression of two infectious diseases in different population. The models exhibit two equilibriums: the equilibrium for a free disease and the endemic. To establish that if the disease free equilibrium is locally asymptotically stable, the fundamental reproductive number (R0) is less than 1. If R0 > 1, the endemic equilibrium exists which is locally asymptotically stable under certain conditions. Numerical simulations suggest that the individual experiencing incident of HIV infections are at a risk of TB co-infection, compared with individuals without HIV infection. This R0<1 (i.e.RT<1 and RH<1) condition is considered to ascertain the stability of the disease free equilibrium E0. It is indicated numerically that the susceptible individuals (yS) converges to the population (N) as t→∞, while the rest of the remaining disease dies out in the population. This R0>1 (RT>1 and RH>1) condition is considerably ascertained the endemic equilibrium stability (E0*).

Keywords: Epidemiology, infection, immunology, prevalence, stability


How to Cite

AZEEZ, A., NDEGE, J., MUTAMBAYI, R., & QIN, Y. (2018). A MATHEMATICAL MODEL FOR TB/HIV CO-INFECTION TREATMENT AND TRANSMISSION MECHANISM. Asian Journal of Mathematics and Computer Research, 22(4), 180–192. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1232

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