| Issue |
Math. Model. Nat. Phenom.
Volume 13, Number 1, 2018
Theory and applications of fractional differentiation
|
|
|---|---|---|
| Article Number | 9 | |
| Number of page(s) | 10 | |
| DOI | https://doi.org/10.1051/mmnp/2018015 | |
| Published online | 06 April 2018 | |
Uniform asymptotic stability of a fractional tuberculosis model
1
Algoritmi Center, University of Minho,
4800-058
Guimarães, Portugal
2
Center of Mathematics, University of Minho,
4800-058
Guimarães, Portugal
3
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro,
3810-193
Aveiro, Portugal
* Corresponding author: delfim@ua.pt
Received:
12
August
2017
Accepted:
22
January
2018
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 α ∈ (0, 1). Numerical simulations for the stability of the endemic equilibrium are provided.
Mathematics Subject Classification: 26A33 / 34C60 / 34D20 / 92C60
Key words: Tuberculosis / fractional differentiation / ordinary differential equations / numerical solutions / stability
© EDP Sciences, 2018
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