Mathematical Model for Coinfection of Hiv/Aids and Kaposi’s Sarcoma with Treatment
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Date
2023
Authors
Juma, Joy Teng’an
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta university
Abstract
HIV destroys T-cells in order to target the body's defence mechanism. Without treatment HIV infection advances in stages causing destruction and reduction in T-cells thus, rendering the body incapable of fighting other infections such as respiratory infections, sexually transmitted diseases and some cancers. Kaposi’s sarcoma is the cancer that allows tumour to grow in an HIV-patient and its presence in a patient is an indication that HIV has fully developed to AIDS in the patient. AIDS-related Kaposi’s sarcoma (AIDS-KS) is still one of the most common malignancies in Kenya and sub-Saharan Africa and is associated with high morbidity and mortality. Researches have indicated that AIDS-associated KS was on the rise in sub-Saharan Africa until the introduction of ART. It is of great significance to comprehend the impact of ART used on HIV/AIDS and the coinfection of HIV/AIDS and AIDS-related Kaposi’s sarcoma. Mathematical models have been proven valuable to give a decisive quantitative information about the dynamics and pathogenesis of HIV, responses of the immunity to anti-retroviral treatment and to the study of the coinfection of HIV/AIDS and other opportunistic infections like Malaria, TB, Pneumonia and Hepatitis however the coinfection of HIV/AIDS and AIDS-related Kaposi’s sarcoma has not been considered much incorporating the aspect of treatment. In this study, a mathematical model for the coinfection of HIV/AIDS and KS with treatment is developed and analysed to explore the effect of usage of ART on HIV/AIDS and the coinfection of HIV/AIDS and Kaposi’s sarcoma. The model solution is explored for positivity and boundedness. The next generation matrix is used to derive the basic reproduction number of the model, while the disease free equilibrium point is determined for stability where it was verified that the infection-free equilibrium 𝐸0 is locally asymptotically stable whenever 𝑅0𝐻<1 and 𝑅0𝐾<1. KS and HIV infection will go to extinction if the reproduction number is < l and persist in the population if it is > 1. Numerical simulations is used to illustrate that by providing treatment to the HIV and the co-infected population immune system is strengthened and thus progression rate to AIDS is reduced.
Description
A Research Project Submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science in Applied Mathematics in the School of Pure and Applied Sciences of Kenyatta University
Keywords
Coinfection of Hiv/Aids, Kaposi’s Sarcoma, Treatment