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We study the spread of susceptible-infected-recovered (SIR) infectiousdiseases where an individual's infectiousness and probability of recoverydepend on his/her "age" of infection. We focus first on early outbreak stageswhen stochastic effects dominate and show that epidemics tend to happen fasterthan deterministic calculations predict. If an outbreak is sufficiently large,stochastic effects are negligible and we modify the standard ordinarydifferential equation (ODE) model to accommodate age-of-infection effects. Weavoid the use of partial differential equations which typically appear inrelated models. We introduce a "memoryless" ODE system which approximates thetrue solutions. Finally, we analyze the transition from the stochastic to thedeterministic phase.

Epidemics with general generation interval distributions