Open AccessA two-strain TB model with multiple latent stages
Author(s) -
Azizeh Jabbari,
Carlos Castillo-Chávez,
Fereshteh Nazari,
Bingbing Song,
Hossein Kheiri
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2016017
Subject(s) - stability theory , basic reproduction number , tuberculosis , mathematics , transmission (telecommunications) , variable (mathematics) , reproduction , strain (injury) , class (philosophy) , stability (learning theory) , computer science , biology , medicine , ecology , mathematical analysis , physics , environmental health , artificial intelligence , population , telecommunications , pathology , quantum mechanics , nonlinear system , anatomy , machine learning
A two-strain tuberculosis (TB) transmission model incorporating antibiotic-generated TB resistant strains and long and variable waiting periods within the latently infected class is introduced. The mathematical analysis is carried out when the waiting periods are modeled via parametrically friendly gamma distributions, a reasonable alternative to the use of exponential distributed waiting periods or to integral equations involving ``arbitrary'' distributions. The model supports a globally-asymptotically stable disease-free equilibrium when the reproduction number is less than one and an endemic equilibriums, shown to be locally asymptotically stable, or l.a.s., whenever the basic reproduction number is greater than one. Conditions for the existence and maintenance of TB resistant strains are discussed. The possibility of exogenous re-infection is added and shown to be capable of supporting multiple equilibria; a situation that increases the challenges faced by public health experts. We show that exogenous re-infection may help established resilient communities of actively-TB infected individuals that cannot be eliminated using approaches based exclusively on the ability to bring the control reproductive number just below 1.