Parameter Estimation of an Epidemic Model with State Constraints.

Area of Science:

• Mathematical modeling
• Epidemiology
• Optimal control theory

Background:

• Mathematical models are crucial for understanding epidemic transmission dynamics.
• Identifying system parameters is essential for accurate disease forecasting and containment.
• Existing methods may not fully account for realistic state constraints in epidemic control.

Purpose of the Study:

• To develop and validate a novel mathematical framework for identifying parameters in a five-compartment epidemic model.
• To incorporate realistic state constraints related to disease containment actions.
• To establish conditions of optimality for the primal and dual systems.

Main Methods:

• Utilizing an optimal control technique to solve a minimization problem for parameter identification.
• Employing an approximating problem to prove the maximum principle by passing to the limit.
• Addressing challenges in dual approximating systems with trajectories of bounded variation.
• Deriving a singular dual backward system with a generalized solution in measure.

Main Results:

• Successfully identified system parameters within a constrained epidemic model.
• Demonstrated the validity of the maximum principle through limit procedures.
• Obtained conditions of optimality for the primal problem.
• Established a novel singular dual backward system with generalized solutions.

Conclusions:

• The developed optimal control approach with state constraints offers a new method for parameter identification in epidemic models.
• This technique provides a more realistic framework for analyzing disease containment strategies.
• The study represents a novel contribution to the literature on mathematical epidemiology and control theory.