How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space

Area of Science:

• Epidemiology
• Mathematical Biology
• Virology

Background:

• Influenza-like infections pose a significant public health challenge.
• Understanding the dynamics of infectious diseases is crucial for effective control strategies.
• Previous models have explored influenza transmission but require further refinement regarding immunity and viral evolution.

Purpose of the Study:

• To extend a mathematical model for influenza-like infection dynamics.
• To investigate the impact of waning acquired immunity and antigenic drift on disease patterns.
• To analyze long-term behaviors under different immunity scenarios.

Main Methods:

• Utilized a previously published mathematical model.
• Incorporated waning immunity and punctuated antigenic drift.
• Employed coupled integral equations within seasons and discrete maps between seasons.
• Examined scenarios where immunity depends on time since last infection or number of infections.

Main Results:

• Immunity waning based on time since last infection led to complex dynamics and multiple attractors.
• Immunity based on the number of infections resulted in a stable fixed point with predictable seasonal epidemics.
• Combining both immunity paradigms predominantly yielded stable fixed points or periodic solutions.
• Stochastic perturbations did not fundamentally alter the model's qualitative dynamics.

Conclusions:

• Host immunity duration significantly influences the predictability of influenza-like epidemics.
• Time-dependent waning immunity can introduce complex and potentially unpredictable epidemiological dynamics.
• Mathematical modeling provides valuable insights into the interplay of immunity, viral drift, and disease transmission patterns.