Epidemics with general generation interval distributions.

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Susceptible-Infected-Recovered (SIR) models are standard for infectious disease spread.
• Individual infectiousness and recovery rates often vary with infection duration (age of infection).
• Stochastic effects significantly influence early-stage epidemics, while deterministic models are suitable for larger outbreaks.

Purpose of the Study:

• To investigate the impact of infection age on SIR disease dynamics.
• To develop a novel mathematical model that incorporates age-of-infection effects without using complex partial differential equations.
• To analyze the transition between stochastic and deterministic phases of an epidemic.

Main Methods:

• Analysis of early outbreak stages dominated by stochastic processes.
• Modification of standard ordinary differential equation (ODE) models to include age-of-infection dependencies.
• Development of a "memoryless" ODE system as an approximation for accurate solutions.

Main Results:

• Stochastic effects cause epidemics to spread faster in early stages than deterministic models predict.
• A novel, memoryless ODE system effectively approximates disease dynamics influenced by infection age.
• The study characterizes the transition from stochastic to deterministic epidemic behavior.

Conclusions:

• Infection age is a critical factor influencing epidemic speed and dynamics.
• The proposed memoryless ODE model offers a computationally efficient alternative to partial differential equations for age-structured epidemic modeling.
• Understanding the interplay between stochasticity and determinism is key to accurate infectious disease forecasting.