  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.
