Optimal control of a Tuberculosis model with state and control delays

2016/06/28 by Cristiana J. Silva, Helmut Maurer, Delfim F. M. Torres · 3 citations
Biochemistry, Genetics and Molecular Biology · Immunology and Microbiology · Mathematics · Medicine · #Active tuberculosis #Artificial intelligence #Computer science #Control (management) #Control theory (sociology) #Immune Cell Function and Interaction #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical optimization #Mathematics #Medicine #Mycobacterium tuberculosis #Optimal control #Pathology #Tuberculin #Tuberculosis #math.OC #msc:34D30 #msc:49M05 #msc:92D30 #msc:93A30 #q-bio.PE

paper · pdf · doi:10.3934/mbe.2017021

published as Math. Biosci. Eng. 14 (2017), no. 1, 321--337 · This 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

arxiv created 2016/06/28 · arxiv updated 2016/10/07 · openalex publication_date 2016/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• A delay-differential equation model of HIV infection of CD4+ T-cells
• Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• The Mathematics of Infectious Diseases

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