A fractional-order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections

In this paper, we propose a fractional-order delay differential model for tuberculosis (TB) transmission with the effects of endogenous reactivation and exogenous reinfections. We investigate the qualitative behaviors of the model throughout the local stability of the steady states and bifurcation analysis. A discrete time delay is introduced in the model to justify the time taken for diagnosis of the disease. Existence and positivity of the solutions are investigated. Some interesting sufficient conditions that ensure the local asymptotic stability of infection-free and endemic steady states are studied. The fractional-order TB model undergoes Hopf bifurcation with respect to time delay and disease transmission rate. The presence of fractional order and time delay in the model improves the model behaviors and develops the stability results. A numerical example is provided to support our theoretical results.

Automated summary

This paper proposes a fractional-order delay differential model for tuberculosis transmission with the effects of endogenous reactivation and exogenous reinfections. Qualitative behaviors of the model, local stability of the steady states, and bifurcation analysis are investigated. The model introduces a discrete time delay to justify diagnosis time, with the existence and positivity of solutions also studied. The fractional-order TB model undergoes Hopf bifurcation with respect to time delay and disease transmission rate, improving model behaviors and stability results. A numerical example is provided to support the theoretical results.