Models for the simple epidemic

Stochastic and deterministic models for the simple epidemic are formulated and compared. Both discrete and continuous time models are considered. The conjecture of equivalence between stochastic and deterministic models for large initial susceptible populations is shown to be of limited practical importance by a simulation study, whereas the number of initial infectives is shown to dramatically affect the convergence of the two types of models. In addition, the discrete stochastic model, which is easy to formulate and simulate, is shown to converge with its continuous counterpart as the time step becomes small.