Fast Stochastic Epidemic Simulations and an Adaptation of the Next Generation Matrix for a Covid-19 Epidemic Model of Social Distancing

Direct stochastic simulations of medium to large scale Markovian processes with population dynamics may have runtimes that are proportional to the population size, if they account for each state transition of each individual in the population. Several approaches to speed up such simulations have been proposed. We use a discrete-time, Euler-forward type approximation for state transition functions that simulates all transitions within a given time step in an effort to improve run times, at the expense of some (potentially correctable) bias. We illustrate this with a stylized model of COVID-19 social distancing interventions in the United Arab Emirates. We also adapt the next generation matrix method of Hill and Longini (2003) to a continuous time, discrete state model. The approach accelerates simulation run times from a linear scaling of run times in population size to a constant that depends on the number of possible state transitions.