Optimal control of pattern formations for an SIR reaction-diffusion epidemic model

Area of Science:

• Mathematical epidemiology
• Infectious disease modeling
• Pattern formation

Background:

• Reaction-diffusion models offer insights into infectious disease transmission dynamics.
• Turing patterns in epidemic models reveal complex spatial-temporal spread.
• Understanding pattern formation is crucial for disease control.

Purpose of the Study:

• To analyze Turing pattern formations in a SIR reaction-diffusion epidemic model.
• To introduce a quantitative indicator (normal serious prevalent area - NSPA) for epidemic extent.
• To develop and validate an optimal control strategy to mitigate epidemic spread.

Main Methods:

• Review of Turing pattern formations in the SIR reaction-diffusion model.
• Introduction and application of the normal serious prevalent area (NSPA) indicator.
• Mathematical formulation and numerical solution of an optimal control problem.
• Numerical experiments to assess control effectiveness.

Main Results:

• The extent of an epidemic is positively correlated with NSPA.
• Optimal control, by adjusting the removed rate, effectively reduces NSPA.
• The proposed control method demonstrates effectiveness in control effect, precision, and cost.

Conclusions:

• Turing patterns in SIR models provide valuable insights into epidemic dynamics.
• NSPA is a useful metric for characterizing epidemic severity and spatial extent.
• Optimal control strategies targeting the removed rate are effective in managing epidemic spread and reducing NSPA.