Incorporating the Pre-symptomatic Stage in the Discrete-Time Kermack-McKendrick Model

Numerous mathematical models have been implemented since the COVID-19 pandemic, with most using large compartmental models which indirectly restrict the generation-time distribution. The continuous-time Kermack-McKendrick epidemic model of 1927 (KM27) allows a random generation-time distribution, but there is a disadvantage where the numerical implementation is too much. Here, the pre-symptomatic stage was further included in the recent discrete-time SEIR KM27 Model formulated in Diekmann (2021). With discrete-time models being general, flexible when including public health interventions and easier to implement computationally than continuous-time models, it is a powerful tool for exploring infectious diseases such as COVID-19. To demonstrate this potential, a numerical investigation is performed on how the incidence-peak size depends on the model components. It was found that compartmental models predicted lower peak sizes with the same reproduction number and initial growth rate than models in which the latent, pre-symptomatically infectious and symptomatically infectious periods have fixed duration.