Nonlinear neural networks adaptive control for a class of fractional-order tuberculosis model

Na Pang; Na Pang

doi:10.3934/mbe.2023461

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 10464-10478. doi: 10.3934/mbe.2023461

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Research article

Nonlinear neural networks adaptive control for a class of fractional-order tuberculosis model

Na Pang ^,

Department of Information and Computing Sciences, Xinhua College of Ningxia University, Yinchuan 750021, China

Received: 18 December 2022 Revised: 15 March 2023 Accepted: 30 March 2023 Published: 07 April 2023

The problem of nonlinear adaptive control for a class of fractional-order tuberculosis (TB) model is studied in this paper. By analyzing the transmission mechanism of TB and the characteristics of fractional calculus, a fractional-order TB dynamical model is established with media coverage and treatment as control variables. With the help of universal approximation principle of radial basis function neural networks and the positive invariant set of established TB model, the expressions of control variables are designed and the stability of error model is analyzed. Thus, the adaptive control method can guarantee that the number of susceptible and infected individuals can be kept close to the corresponding control targets. Finally, the designed control variables are illustrated by numerical examples. The results indicate that the proposed adaptive controllers can effectively control the established TB model and ensure the stability of controlled model, and two control measures can protect more people from tuberculosis infection.
- fractional-order tuberculosis model,
- adaptive control,
- media coverage,
- treatment
Citation: Na Pang. Nonlinear neural networks adaptive control for a class of fractional-order tuberculosis model[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10464-10478. doi: 10.3934/mbe.2023461

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Abstract

The problem of nonlinear adaptive control for a class of fractional-order tuberculosis (TB) model is studied in this paper. By analyzing the transmission mechanism of TB and the characteristics of fractional calculus, a fractional-order TB dynamical model is established with media coverage and treatment as control variables. With the help of universal approximation principle of radial basis function neural networks and the positive invariant set of established TB model, the expressions of control variables are designed and the stability of error model is analyzed. Thus, the adaptive control method can guarantee that the number of susceptible and infected individuals can be kept close to the corresponding control targets. Finally, the designed control variables are illustrated by numerical examples. The results indicate that the proposed adaptive controllers can effectively control the established TB model and ensure the stability of controlled model, and two control measures can protect more people from tuberculosis infection.

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