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

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.