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DOI: 10.23952/jnfa.2020.15
Received November 29, 2019; Accepted April 6, 2020; Published April 24, 2020
Abstract. In this paper, a fractional-order mathematical model with control is constructed to describe the transmission of tuberculosis. Two cases are considered: the constant control and the optimal control. In the former case, the stability conditions of the disease-free equilibrium and the endemic equilibrium are obtained. In the second case, optimal control theory is applied to the corresponding model. The optimal control formula is derived by use of the Hamiltonian function and the Pontryagin’s Maximum Principle. In addition, some numerical simulations are performed to support our analytic results.
How to Cite this Article:
Ruiqing Shi, Jianing Ren, Cuihong Wang, Analysis of a fractional order mathematical model for tuberculosis with optimal control, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 15, pp. 1-18.