paper

Optimal Control of a Tuberculosis Model with State and Control Delays

arXiv:1606.08721 · doi:10.3934/mbe.2017021

Abstract

We introduce delays in a tuberculosis (TB) model, representing the time delay on the diagnosis and commencement of treatment of individuals with active TB infection. The stability of the disease free and endemic equilibriums is investigated for any time delay. Corresponding optimal control problems, with time delays in both state and control variables, are formulated and studied. Although it is well-known that there is a delay between two to eight weeks between TB infection and reaction of body's immune system to tuberculin, delays for the active infected to be detected and treated, and delays on the treatment of persistent latent individuals due to clinical and patient reasons, which clearly justifies the introduction of time delays on state and control measures, our work seems to be the first to consider such time-delays for TB and apply time-delay optimal control to carry out the optimality analysis.

arXiv commentThis is a preprint of a paper whose final and definite form will be published in the journal 'Mathematical Biosciences and Engineering', ISSN 1547-1063 (print), ISSN 1551-0018 (online). Submitted 30/Oct/2015; revised 24/May/2016; accepted for publication 26/Jun/2016

References in corpus (3)

Cited by in corpus (19)