Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 61, Issue -, Pages 104-126Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2018.01.012
Keywords
HIV; TB; Multi-drug resistant strains; Fractional order model
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Funding
- European Regional Development Fund through the program COMPETE
- Portuguese Government through the FCT - Fundacao para a Ciencia e a Tecnologia [PEst-C/MAT/UI0144/2013]
- FCT [SFRH/BD/96816/2013]
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We study the impact of diabetes and multi-drug resistant strains in a non-integer order model for tuberculosis (TB) infection in a community. We compute the reproduction number, R-0, of the model and analyse its behaviour numerically for variation of epidemiologically relevant parameters. Namely, the increased susceptibility to TB due to diabetes, the diabetes recruitment rate, and the increased progression of non-diabetics TB infectious to diabetic TB infectious individuals, due to their active TB status. We have proven the global stability of the disease-free equilibrium for specific conditions, related with exogeneous and endogeneous reinfections, and relapse of recovered individuals. Numerical simulations of the model for the above mentioned parameters confirm the dynamics predicted by the value of R-0. For R-0 < 1 the disease-free equilibrium is stable, and it becomes unstable for R-0 > 1. The sensitivity indexes of R-0 are computed and discussed. The order of the fractional derivative adds more information about the complexity of the dynamics of the proposed model and may help distinguishing dynamical traits in distinct TB patients. (C) 2018 Elsevier B.V. All rights reserved.
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