Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model

Tingting Xue (), Xiaolin Fan and Yan Xu
Additional contact information
Tingting Xue: School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China
Xiaolin Fan: School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China
Yan Xu: School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China

Mathematics, 2023, vol. 11, issue 17, 1-18

Abstract: The fractional-order calculus model is suitable for describing real-world problems that contain non-local effects and have memory genetic effects. Based on the definition of the Caputo derivative, the article proposes a class of fractional hepatitis B epidemic model with a general incidence rate. Firstly, the existence, uniqueness, positivity and boundedness of model solutions, basic reproduction number, equilibrium points, and local stability of equilibrium points are studied employing fractional differential equation theory, stability theory, and infectious disease dynamics theory. Secondly, the fractional necessary optimality conditions for fractional optimal control problems are derived by applying the Pontryagin maximum principle. Finally, the optimization simulation results of fractional optimal control problem are discussed. To control the spread of the hepatitis B virus, three control variables (isolation, treatment, and vaccination) are applied, and the optimal control theory is used to formulate the optimal control strategy. Specifically, by isolating infected and non-infected people, treating patients, and vaccinating susceptible people at the same time, the number of hepatitis B patients can be minimized, the number of recovered people can be increased, and the purpose of ultimately eliminating the transmission of hepatitis B virus can be achieved.

Keywords: fractional calculus; Caputo derivative; hepatitis B model; basic reproduction number; stability; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/17/3642/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/17/3642/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:17:p:3642-:d:1223486

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().