Solution of epidemic models with quenched transients

Area of Science:

• Epidemiology
• Mathematical Biology
• Theoretical Ecology

Background:

• Classical epidemiological models like SEI assume constant infection rates.
• Real-world epidemics often exhibit complex dynamics, including changes in host susceptibility and infectiousness over time.
• Standard equilibrium analysis is insufficient for neutrally stable epidemic states.

Purpose of the Study:

• To develop a novel mathematical model for single-season disease epidemics incorporating time-varying infection rates.
• To analyze the
• quenched transient
• epidemic state characterized by decaying host susceptibility.
• To derive an approximate analytical solution for this complex epidemic state.

Main Methods:

• Development of a modified susceptible-exposed-infected (SEI) model with time-dependent primary and secondary infection rates.
• Introduction of a novel analytical method involving interpolation between exactly solvable limits.
• Application of the method across the model's five-dimensional parameter space.

Main Results:

• The model accurately captures epidemic slowdown and cessation due to decaying host susceptibility.
• A unique
• quenched transient
• state is identified, dependent on the epidemic's history.
• An approximate analytical solution for this neutrally stable state is successfully derived.

Conclusions:

• The developed model provides a more realistic framework for studying single-season epidemics.
• The novel analytical method offers insights into epidemic dynamics not accessible by traditional equilibrium analysis.
• The findings have potential applications in understanding and managing real-world disease outbreaks.