Modelling the impact of precaution on disease dynamics and its evolution

Area of Science:

• Epidemiology
• Mathematical Modeling
• Behavioral Science

Background:

• Public health interventions are crucial for epidemic control.
• Understanding the interplay between epidemic severity and public behavior is essential.
• Existing models often simplify public response to disease outbreaks.

Purpose of the Study:

• To introduce a novel framework modeling epidemic dynamics with evolving public precaution levels.
• To analyze the impact of behavioral responses on disease spread and long-term dynamics.
• To provide a theoretical basis for understanding adaptive public health strategies.

Main Methods:

• Developed a general framework model for epidemic dynamics with a practically susceptible population.
• Assumed the fraction of susceptible individuals depends on epidemic severity and public precaution.
• Analyzed model well-posedness and disease vanishing for basic reproduction number < 1.
• Investigated disease dynamics under instantaneous and delayed best response behavioral models.

Main Results:

• Confirmed disease extinction when the basic reproduction number is less than 1.
• Demonstrated that behavioral responses significantly influence epidemic dynamics.
• Showed that instantaneous best response leads to endemic equilibrium.
• Identified that delayed best response can result in convergence to equilibrium or periodic solutions.

Conclusions:

• The proposed framework offers a more realistic representation of epidemic spread by including evolving public behavior.
• The study provides mathematical justification for the use of best response functions in epidemiological models.
• Adaptive dynamics, rather than fixed responses, may better explain long-term epidemic patterns.