Optimal and adaptive control of an epidemic model of influenza with unknown parameters

Authors

  • Hassan Saberi Nik Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, ‎Iran
  • Tolu Zarasvand Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, ‎Iran

DOI:

https://doi.org/10.30495/jme.v11i0.516

Keywords:

‎Optimal control, Influenza, Epidemic model, Lyapunov function, Pontryagin's maximum principle.

Abstract

This paper deals with the nonlinear dynamics‎, ‎chaos‎, ‎optimal and adaptive control of an epidemic model for H1N1 influenza with unknown parameters‎. ‎Two different control strategies are explored‎. ‎First‎, ‎we use the optimal control theory to reduce the infected individuals and the cost of

vaccination‎. ‎Then‎, ‎we study the problem of optimal control of unstable steady-states of H1N1 influenza system using a nonlinear‎

‎control approach‎. ‎Finally‎, ‎we propose the Lyapunov stability to control of the chaotic epidemic model of influenza with unknown parameters by a feedback control approach‎. ‎Matlab bvp4c and ode45 have been used for solving the autonomous chaotic systems and the extreme conditions obtained from the Pontryagin's maximum principle (PMP)‎. ‎Furthermore‎, ‎numerical simulations are included to demonstrate the effectiveness of the proposed control strategies.

Author Biography

Hassan Saberi Nik, Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, ‎Iran

Hassan Saberi Nik
serves as a Lecturer at the Department of Mathematics in Islamic Azad University,
Neyshabur Branch, Neyshabur, Iran. He acquired
his Ph.D. degree in numerical analysis at Ferdowsi
University of Mashhad, Mashhad, Iran. His main research interests are in the computational methods of optimal control, chaos control and iterative methods for solving differential equations with emphasis on the spectral homotopy analysis method.

He now lives at Stockholm in Sweden.

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Published

2017-08-02

Issue

Vol. 11

Section

Vol. 11, No. 3, (2017)

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