TITLE:
SIR Model and HIV/AIDS in Khartoum
AUTHORS:
Sheima M. E. Abueldahab, Franck Kalala Mutombo
KEYWORDS:
Acquired Immunodeficiency Syndrome (AIDS), Human Immunodeficiency Virus (HIV), SIR Deterministic Model, The Reproduction Number (R0), Antiretroviral Treatment (ART)
JOURNAL NAME:
Open Access Library Journal,
Vol.8 No.4,
April
30,
2021
ABSTRACT: The Human Immunodeficiency Virus (HIV) epidemic in Khartoum constitutes the most serious health problem in the region and one that we do not fully understand. Recent approaches aiming to understand the situation have attempted to model the Human Immunodeficiency Virus (HIV) epidemic using deterministic compartmental models. Our work has reviewed the formal mathematical work on deterministic models of this nature and considers the relevance of the modelling approach to the HIV in Khartoum. This model is built on SIR and population models. Evaluation of the basic reproduction number, R0, will be carried out using the SIR model for an optimal value of α and γ where α and γ are the inflow and the outflow of infectious individuals per infectious capita respectively (R0 = α γ ). The population will be divided into compartments, in- and out-flows from compartments leading to a corresponding differential equation. A numerical solver in MATLAB is then used to compute the solutions. Our model will be fitted to the data from Khartoum state, which is the capital of the Sudan and it has very good data related to HIV. Our results demonstrated that Khartoum was endemic for HIV when the epidemic began in the year 2002 until the year 2005 (R0 is 1.02). The value of R0 decreases and remains stable for ten years from the year 2006-2016 (R0 is 0.98). The most affected Sudanese population in Khartoum with AIDS was the male (Teenager) 10 - 19 age group. Also the treatment (ART) is recommended for everyone who had HIV.