Mathematical Analysis of the Transmission Dynamics of HIV/AIDS: Role of Female Sex Workers

Abstract

Abstract:The transmission of 'Human Immunodeficiency Virus (HIV)' that causes the 'Acquired Immunodeficiency Syndrome (AIDS)' is strongly associated with un-protected sex and at the present understanding this epidemic can reach higher prevalence threshold level when there are extensive sexual contacts between the sex workers and general population. In the present work, we investigate a nonlinear model for studing the transmission dynamics of HIV/AIDS epidemic with emphasis on the role of female sex workers. Here, we consider only the heterosexual transmissions of HIV/AIDS and formulate the mathematical model by dividing the total adult population under consideration into three different classes: male, female and female sex workers. We assume different rates of recruitment for different classes of the population. The equilibria of the model and their stability are discussed in detail. The basic reproduction number R 0 of the model is computed and it is shown that the disease-free equilibrium is stable only when R 0 < 1. When the associated reproduction number R 0 > 1, the endemic equilibrium is globally stable. Finally, the numerical simulations are reported to support the presented analytical results.

Analisis Kestabilan Model Epidemi Sjat Pada Penyebaran Penyakit Aids Di Kecamatan Pujer Kabupaten Bondowoso

“…Bilangan Reproduksi Dasar Menurut van den Driessche and Watmough, 2008 "bilangan reproduksi dasar adalah bilangan yang menyatakan rata-rata banyaknya individu rentan yang terinfeksi secara langsung oleh individu terinfeksi dalam populasi rentan". Teorema 3.4 (Kaur et al, 2014) Titik kesetimbangan bebas penyakit 𝑃 𝑜 sistem 2.5 adalah stabil asimtotik lokal ketika 𝑅 0 < 1 dan tidak stabil jika sebaliknya.…”

Mathematical analysis of sex-structured population model of HIV infection in Kenya

“…In the recent years, quite a number of mathematical models have been developed to investigate the dynamics of HIV transmission and spread in the population (Athithan & Ghosh, 2014;Baryarama, Mugisha, & Luboobi, 2006;Doyle, Greenhalgh, & Blythe, 1998;Kaur, Ghosh, & Bhatia, 2014;Okango, Mwambi, & Ngesa, 2016;Omondi, Mbogo, & Luboobi, 2018b;Van Sighem et al, 2012;Wodarz & Nowak, 2002). However, to the authors knowledge, none of these existing mathematical models has explicitly considered incorporating sexual orientation of individuals using real-time series of HIV infection trend data.…”