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" Mathematical Analysis of TB-HIV Co-infection: "
Femi, Abimbade Sulaimon
Ibrahim, Md. O.
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Latin Dissertation
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| Language of Document
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English
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| Record Number
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1105838
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| Doc. No
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TLpq2329730247
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| Main Entry
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Femi, Abimbade Sulaimon
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Ibrahim, Md. O.
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| Title & Author
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Mathematical Analysis of TB-HIV Co-infection:\ Femi, Abimbade SulaimonIbrahim, Md. O.
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| College
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Kwara State University (Nigeria)
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| Date
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2019
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| student score
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2019
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| Degree
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M.S.
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| Page No
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174
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| Abstract
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Tuberculosis (TB) with Human Immunodeficiency Virus (HIV) co-infection in individuals remains a major global health challenge with an estimated 1.4million patients worldwide, despite all the efforts put in place by the World health Organization (WHO) in order to curtail the dynamical spread of TB-HIV Coinfection. The synergistic effect of TB with HIV is of great concern in both developing and developed countries which poses high mortality rate in a population. The menace of the co-infection of these two infectious diseases has attracted the attention of many scientists in the recent past. In this study, a mathematical model that describes the epidemiological features of the dynamical spread of TB-HIV coinfection is formulated and analyzed. A deterministic model for TB-HIV co-infection was developed using a system of ordinary differential equation (ODE). Sub-models of TB, HIV and there Coinfection were considered. Positivity and boundedness of solutions of the co-infection model was investigated. The existence and uniqueness of solution for each of the models for TB, HIV and their co-infection exist. The equilibrium states for the models were analyzed. The basic reproduction numbers for the models R0T, R0H, and R0 were computed using Next Generation Matrix Method (NGM) and Graph Theoretic Method (GTM). The stability of disease free equilibrium points for TB, HIV and the co-infection model were determined. Sensitivity analyses for TB, HIV and coinfection models were performed. Numerical simulations were carried out by MAPLE 18 software to determine the best preventive or control measure to be adopted in curtailing the dynamical spread of TB, HIV and their co-infection. The stability analysis reveals that the disease free equilibrium points for TB, HIV and their co-infection models were locally asymptotically stable whenever the basic reproduction numbers R0T, R0H, and R0 is less than unity and unstable if otherwise. The sensitivity analysis carried out revealed that the effective contact rate (βT) for Tuberculosis and effective contact rate (βH) for Human Immunodeficiency Virus for the co-infection model are very sensitive and have a pronounced effect on their respective basic reproduction numbers. This study concluded that, epidemiological features such as proper education or public awareness, minimization of effective contact rate and effective treatment of infectious individuals plays a pertinent role in the control of the dynamical spread of TB-HIV co-infection.
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Epidemiology
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Mathematics
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Microbiology
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Public health education
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