Butt, A.I.K. Atangana-Baleanu Fractional Dynamics of Predictive Whooping Cough Model with Optimal Control Analysis. Symmetry2023, 15, 1773.
Butt, A.I.K. Atangana-Baleanu Fractional Dynamics of Predictive Whooping Cough Model with Optimal Control Analysis. Symmetry 2023, 15, 1773.
Butt, A.I.K. Atangana-Baleanu Fractional Dynamics of Predictive Whooping Cough Model with Optimal Control Analysis. Symmetry2023, 15, 1773.
Butt, A.I.K. Atangana-Baleanu Fractional Dynamics of Predictive Whooping Cough Model with Optimal Control Analysis. Symmetry 2023, 15, 1773.
Abstract
In this study, we construct a new Atangana-Baleanu fractional model for whooping cough
disease to predict future dynamics of the disease, as well as to suggest strategies to eliminate the
disease in an optimal way. We prove that the proposed model has a unique solution which is positive
and bounded. To measure contagiousness of the disease, we determine the reproduction number
R0 and use it to examine the local and global stability at equilibrium points that have symmetry.
Through sensitivity analysis, we determine parameters of the model that are most sensitive to R0.
The ultimate aim of this research is to analyze different disease prevention approaches in order to
find the most suitable one. For this, we include the vaccination and quarantine compartments in
the proposed model and formulate an optimal control problem to assess the effect of vaccination
and quarantine rates on disease control in three distinct scenarios. Firstly, we study the impact of
vaccination strategy and conclude findings with presentation of graphical results. Secondly, we
examine the impact of quarantine strategy on whooping cough infection with possible elimination
from the society. Lastly, we implement vaccination and quarantine strategies together to visualize
their combine effect on infection control. In addition to the study of an optimal control problem,
we examine the effect of fractional order on disease dynamics as well as the impact of constant
vaccination and quarantine rates on disease transmission and control. We determine that the optimal
control strategy with the three controls is more effective in reducing the spread of whooping cough
infection. Implementation of Toufik-Atangana type numercial scheme both for the state and adjoint
equations is another contribution of this article.
Keywords
whooping cough; atangana-Baleanu derivative; vaccination; existence and uniqueness; stability and sensitivity analysis; toufik-atangana scheme; optimal control
Subject
Computer Science and Mathematics, Mathematical and Computational Biology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The commenter has declared there is no conflict of interests.
Commenter:
The commenter has declared there is no conflict of interests.
Commenter:
The commenter has declared there is no conflict of interests.