On discrete time epidemic models in Kermack-McKendrick form

ABSTRACT

Surprisingly, the discrete-time version of the general 1927 Kermack-McKendrick epidemic model has, to our knowledge, not been formulated in the literature, and we rectify this omission here. The discrete time version is as general and flexible as its continuous-time counterpart, and contains numerous compartmental models as special cases. In contrast to the continuous time version, the discrete time version of the model is very easy to implement computationally, and thus promises to become a powerful tool for exploring control scenarios for specific infectious diseases. To demonstrate the potential, we investigate numerically how the incidence-peak size depends on model ingredients. We find that, with the same reproduction number and initial speed of epidemic spread, compartmental models systematically predict lower peak sizes than models that use a fixed duration for the latent and infectious periods.