Optimal control theory of an age‐structured coronavirus disease model and the dynamical analysis of the underlying ordinary differential equation model having constant parameters

This paper addresses the dynamics of COVID‐19 using the approach of age‐structured modeling. A particular case of the model is presented by taking into account age‐free parameters. The sub‐model consisting of ordinary differential equations (ODEs) is investigated for possible equilibria, and qualita...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-01, Vol.47 (2), p.660-679
Main Authors: Ibrahim, Muhammad, Khan, Asaf, Allehiany, F. M., Zaman, Gul, Ali, Vakkar, Saeed, Tareq
Format: Article
Language:English
Subjects:
age structured
Control theory
Differential equations
Disease control
Mathematical models
Maximum principle
novel coronavirus
Optimal control
optimal control theory
Parameters
simulation
stability analysis
Viral diseases
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Summary:This paper addresses the dynamics of COVID‐19 using the approach of age‐structured modeling. A particular case of the model is presented by taking into account age‐free parameters. The sub‐model consisting of ordinary differential equations (ODEs) is investigated for possible equilibria, and qualitative aspects of the model are rigorously presented. In order to control the spread of the disease, we considered two age‐ and time‐dependent non‐pharmaceutical control measures in the age‐structured model, and an optimal control problem using a general maximum principle of Pontryagin type is achieved. Finally, sample simulations are plotted which support our theoretical work.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9675