An Approach to Estimating the Transmission Coefficients for AIDS and for Tuberculosis Using Mathematical Models

Abstract

A mathematical model is presented to simulate the interaction between Human Immunodeficiency Virus (HIV) and Mycobacterium tuberculosis (MTB) infections in a closed environment. The dynamics is formulated through a compartmental system of non-linear ordinary differential equations. The stability of the trivial equilibrium point or absence of infections and the endemic basins are analyzed based on the threshold values for the HIV and MTB transmission coefficients. In order to deal with the estimation of the transmission coefficients of HIV and MTB infections we consider the incarcerated individuals in the Female Penitentiary of Sa˜o Paulo State, Brazil.

Modeling the joint epidemics of TB and HIV in a South African township

“…Augmenter la détection et le traitement de la tuberculose plus efficace que d'autres interventions. [57] Analyse mathématique pour le Brésil de 3 × 3 − 2 = 7 EDO. Stabilité deséquilibres.…”

“…[58] Analyse mathématique de Tous ces modèles contiennent de nombreux paramètres inconnus mais reposent sur peu de données. Par exemple, il semblerait que [14,15,32,57,70] soient les seulsà ajuster leurs paramètres aux séries temporelles de la prévalence du VIH (des cas de SIDA dans [70]) et des notifications de la tuberculose. Pour le bidonville sud-africain de notreétude, on a deux informations supplémentaires : le pourcentage de personnes séropositives parmi les cas de tuberculose notifiés et la prévalence de la tuberculoseà une date.…”

Mathematical epidemiology: Past, present, and future

“…Another possible situation is coinfection of more than one disease requiring more elaborate models. This is a real possibility with HIV and tuberculosis ( Kirschner, 1999 , Naresh and Tripathi, 2005 , Porco et al., 2001 , Raimundo et al., 2003 , Schulzer et al., 1994 , West and Thompson, 1997 ).…”

An investigation into the statistical properties of TB episodes in a South African community with high HIV prevalence

“…Some evaluate the potential impact of control strategies advocated by the World Health Organization (WHO) (Dye et al, 1998;Murray and Salomon, 1998). A small subset (Currie et al, 2003(Currie et al, , 2005Hughes et al, 2006;Raimundo et al, 2003;West and Thompson, 1997) provides guidance for fitting models to real time-series data of HIV-TB epidemics. Drawing particularly upon these works, Bacaër et al developed and tailored a model to the HIV-TB epidemic in Masiphumelele.…”