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The reinfection threshold, revisited.

F M G Magpantay1, J Mao2, S Ren1

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Leaky immunity, where recovery doesn't fully prevent reinfection, has a critical threshold. This threshold impacts disease modeling and parameter estimation, especially for acute infections with imperfect immunity.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Immunology

Background:

  • Infection-derived immunity can be imperfect, leading to a non-zero risk of reinfection, termed leaky immunity.
  • The degree of leakiness is quantified by the relative probability of reinfection for previously infected versus naive individuals.
  • A reinfection threshold has been proposed, but its significance and existence have been debated.

Purpose of the Study:

  • To investigate the mathematical and epidemiological significance of the reinfection threshold in models of leaky immunity.
  • To explore the relationship between the reinfection threshold and critical points in disease dynamics.
  • To assess the impact of the reinfection threshold on parameter estimation in epidemiological models.

Main Methods:

  • Mathematical modeling of infectious disease dynamics with leaky immunity.
  • Analysis of endemic equilibrium stability and rate of prevalence change.
  • Simulation studies to evaluate parameter identifiability.

Main Results:

  • The reinfection threshold is linked to changes in endemic equilibrium stability (stable spiral to stable node) and the peak rate of prevalence change relative to leakiness.
  • These occurrences align closely with the reinfection threshold when the recovery period is short relative to lifespan.
  • Parameter estimation for basic reproduction number is less identifiable for values above the reinfection threshold compared to those below it.

Conclusions:

  • The reinfection threshold is a significant feature in models of imperfect immunity, influencing disease dynamics and predictability.
  • Understanding this threshold is crucial for accurate epidemiological modeling and parameter estimation, particularly for acute infections.
  • The study highlights the importance of considering leaky immunity and its associated threshold in public health interventions and research.