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Effect of optimal control on SI epidemic model
1Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Buraydah, Saudi Arabia.
Scientific Reports
|July 20, 2026
Summary
This study uses optimal control to minimize infections in an SI epidemic model. The dynamic control strategy effectively reduces disease spread and costs, enhancing public health management.
Area of Science:
- Epidemiology
- Control Theory
- Mathematical Biology
Background:
- Epidemic modeling is crucial for understanding disease dynamics.
- Optimal control offers a framework for managing infectious diseases efficiently.
- Previous models often lack dynamic control strategies for minimizing infections and costs.
Purpose of the Study:
- To analyze an optimal control strategy for a susceptible-infected (SI) epidemic model.
- To minimize the number of infected individuals while reducing intervention costs.
- To introduce and analyze a dynamic control variable representing preventive measures.
Main Methods:
- Formulation of SI model dynamics using nonlinear differential equations.
- Application of Pontryagin's Maximum Principle to establish optimal control existence.
- Derivation of adjoint system and optimality conditions.
- Numerical computation using the forward-backward sweep method.
Main Results:
- Optimal control significantly reduces infection levels.
- The strategy maintains a high proportion of susceptible individuals.
- Cost-effectiveness analysis demonstrates practical applicability.
Conclusions:
- Optimal control theory is effective for efficient disease management.
- Dynamic control variables enhance epidemic intervention strategies.
- The SI model with optimal control provides a valuable tool for public health.
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