Epidemics with general generation interval distributions

TL;DR

This paper investigates the dynamics of SIR epidemics with variable infectiousness and recovery based on infection age, introducing a memoryless ODE model to better predict outbreak timing and transition phases.

Contribution

It develops a novel memoryless ODE framework for age-dependent SIR models, avoiding PDEs and capturing stochastic-to-deterministic transition effects.

Findings

Epidemics tend to occur faster than deterministic models predict in early stages.

The memoryless ODE provides accurate approximations of true epidemic dynamics.

Transition analysis clarifies when stochastic effects become negligible.

Abstract

We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic effects dominate and show that epidemics tend to happen faster than deterministic calculations predict. If an outbreak is sufficiently large, stochastic effects are negligible and we modify the standard ordinary differential equation (ODE) model to accommodate age-of-infection effects. We avoid the use of partial differential equations which typically appear in related models. We introduce a "memoryless" ODE system which approximates the true solutions. Finally, we analyze the transition from the stochastic to the deterministic phase.