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Optimal bang-bang control for variable-order dengue virus; numerical studies.

N H Sweilam1,2, S M Al-Mekhlafi1,2, S A Shatta3

  • 1Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.

Journal of Advanced Research
|September 6, 2021
PubMed
Summary

This study optimized dengue virus control using variable-order fractional calculus and bang-bang control, significantly reducing viral load. Numerical methods effectively simulated this optimal control strategy for dengue infection management.

Keywords:
Bang-bang controlDengue virusNonstandard generalized Euler methodNonstandard generalized fourth order Runge-kutta methodVariable order fractional model

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Area of Science:

  • Mathematical Modeling
  • Infectious Disease Dynamics
  • Control Theory

Background:

  • Dengue fever is a significant mosquito-borne viral illness.
  • Mathematical models are crucial for understanding viral replication and immune response.
  • Antibodies play a vital role in controlling viral infections.

Purpose of the Study:

  • To investigate optimal control for a novel variable-order nonlinear dengue virus model.
  • To minimize dengue viral infection and promote rapid virus clearance using bang-bang control.
  • To analyze the impact of variable-order fractional derivatives on modeling time-dependent systems.

Main Methods:

  • Application of Pontryagin's maximum principle with bang-bang control.
  • Development and implementation of two numerical schemes: nonstandard generalized Euler and fourth-order Runge-Kutta methods.
  • Utilizing Caputo's definition for variable-order fractional derivatives.

Main Results:

  • Successfully reduced viremia levels by incorporating DI particles and bang-bang control.
  • The nonstandard generalized fourth-order Runge-Kutta method demonstrated superior performance compared to the Euler method.
  • Variable-order fractional derivatives effectively capture long-range memory effects in dynamic systems.

Conclusions:

  • Combining variable-order fractional derivatives with bang-bang control enhances dengue mathematical model dynamics.
  • The presented numerical methods offer a straightforward approach to solving variable-order fractional optimal control problems.
  • This approach provides a promising strategy for managing dengue virus infections.