Non-integer order analysis of the impact of diabetes and resistant strains in a model for TB infection

• Published in: Communications in nonlinear science & numerical simulation Vol. 61; pp. 104 - 126
• Main Authors: Carvalho, Ana R.M., Pinto, Carla M.A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2018; Elsevier Science Ltd
• Subjects: Computer simulation; Diabetes; Disease prevention; Epidemiology; Fractional order model; HIV; Impact analysis; Impact resistance; Mathematical models; Multi-drug resistant strains; Multidrug resistant organisms; Parameters; Tuberculosis; HIV; Multi-drug resistant strains; TB; Fractional order model
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2018.01.012

•Study the impact of diabetes and multi-drug resistant strains in a model for tuberculosis (TB) infection in a community.•Compute the reproduction number, R0, of the model.•Analyse its behaviour numerically for variation of epidemiologically relevant parameters.•The order of the fractional derivative adds more information on the dynamics of the model. 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, R0, 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 R0. For R0 < 1 the disease-free equilibrium is stable, and it becomes unstable for R0 > 1. The sensitivity indexes of R0 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.