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Global Analysis and Optimal Control Model of COVID-19
Sacrifice Nana-Kyere1, Francis Agyei Boateng1, Paddy Jonathan1
1Deparment of Mathematics and Information Technology, Valley View University, Ghana.
Computational and Mathematical Methods in Medicine
|February 7, 2022
Summary
This study analyzes the SEQIAHR model for COVID-19 dynamics, using mathematical modeling to find optimal control strategies like vaccination and personal protection to minimize the pandemic. The research explores disease spread and stability, offering insights for public health interventions.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- COVID-19 pandemic necessitates understanding disease dynamics for effective control.
- Mathematical models are crucial for analyzing epidemic spread and informing public health strategies.
Purpose of the Study:
- To analyze the dynamics of the SEQIAHR compartmental model for COVID-19.
- To identify optimal control strategies, including personal protection and vaccination, to minimize disease transmission.
- To investigate the stability and bifurcation behavior of the COVID-19 model.
Main Methods:
- Utilized the Castillo-Chavez method and Lyapunov functions for stability analysis.
- Calculated the basic reproduction number (R0) and performed sensitivity analysis.
- Formulated and solved an optimal control model using Pontryagin's maximum principle.
- Employed numerical simulations to evaluate different control strategy combinations.
Main Results:
- Determined the existence and stability of disease-free and endemic equilibria.
- Identified key parameters influencing disease transmission through sensitivity analysis.
- Demonstrated the effectiveness of combined personal protection and vaccination strategies in simulations.
Conclusions:
- The SEQIAHR model provides valuable insights into COVID-19 dynamics.
- Optimal control strategies, particularly vaccination and personal protection, are vital for pandemic containment.
- Mathematical modeling is essential for developing evidence-based public health interventions against infectious diseases.
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