Uniform asymptotic stability of a fractional tuberculosis model

TL;DR

This paper introduces a fractional-order TB transmission model using Caputo derivatives, proving the uniform asymptotic stability of its endemic equilibrium for all fractional orders between 0 and 1, supported by numerical simulations.

Contribution

It presents a novel fractional-order TB model and establishes the stability of its endemic equilibrium for all fractional orders, extending previous integer-order models.

Findings

Proves uniform asymptotic stability for the fractional TB model

Validates stability through numerical simulations

Extends stability analysis to all fractional orders in (0,1)

Abstract

We propose a Caputo type fractional-order mathematical model for the transmission dynamics of tuberculosis (TB). Uniform asymptotic stability of the unique endemic equilibrium of the fractional-order TB model is proved, for any $\alpha \in (0, 1)$. Numerical simulations for the stability of the endemic equilibrium are provided.