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Epidemic models are used to analyze the progression or outcome of an epidemicunder different control policies like vaccinations, quarantines, lockdowns, useof face-masks, pharmaceutical interventions, etc. When these models accuratelyrepresent real-life situations, they may become an important tool in thedecision-making process. Among these models, compartmental models are verypopular and assume individuals move along a series of compartments thatdescribe their current health status. Nevertheless, these models are mostlyMarkovian, that is, the time in each compartment follows an exponentialdistribution. In epidemic models, exponential sojourn times are most of thetimes unrealistic, for instance, they imply that the probability that a patientwill recover from some disease in the next time unit is independent of the timethe patient has been sick. This is an important restriction that prevents thesemodels from being widely accepted and trusted by decision-makers. In spite ofthe need to incorporate algorithms to tackle the problem, literature on thetopic is scarce. Here, we introduce a novel approach to simulate generalstochastic epidemic models that accepts any distribution for the sojourn timesthat is efficient.

The Poisson algorithm: a simple method to simulate stochastic epidemic models with generally distributed residence times