Using continuous-time random walks and gamma inter-event times, the authors derive effective master equations for non-Markovian SIR and SIS models and obtain analytical predictions for final outbreak sizes, quasistationary distributions, and disease lifetimes.
Ovaskainen, The quasistationary distribution of the stochastic logistic model, Journal of Applied Probability 38, 898 (2001)
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Large deviations in non-Markovian stochastic epidemics
Using continuous-time random walks and gamma inter-event times, the authors derive effective master equations for non-Markovian SIR and SIS models and obtain analytical predictions for final outbreak sizes, quasistationary distributions, and disease lifetimes.