Incorporating changeable attitudes toward vaccination into compartment models for infectious diseases

Area of Science:

• Epidemiology
• Mathematical Modeling
• Public Health

Background:

• Understanding disease spread dynamics is crucial for effective public health interventions.
• Vaccination attitudes significantly impact herd immunity and disease transmission.
• Existing models often do not fully capture the feedback loop between disease prevalence and public opinion on vaccination.

Purpose of the Study:

• To develop a mechanistic model integrating epidemiological status (SIR) and vaccination attitudes (Willing/Unwilling).
• To investigate how evolving public opinion on vaccination influences disease spread.
• To analyze the stability of disease-free and endemic equilibria under changing attitudes.

Main Methods:

• Development of a compartmental model classifying individuals by SIR status and vaccination stance.
• Analytical investigation of model equilibria and their stability criteria.
• Numerical simulations to validate analytical findings and explore dynamic behaviors.

Main Results:

• Identification of conditions for disease-free and endemic equilibria.
• Demonstration that attitude shifts driven by disease prevalence can destabilize endemic states.
• Observation of limit cycle oscillations resulting from attitude-induced destabilization.

Conclusions:

• Public vaccination attitudes are a critical factor in disease dynamics, capable of altering epidemic trajectories.
• Disease prevalence can create feedback loops that dynamically change vaccination willingness, impacting long-term disease control.
• The model provides a framework for understanding how dynamic public opinion can lead to complex, cyclical epidemic patterns.