Figure 14.

The COVID-19 disease model with both unvaccinated and vaccinated states. This disease progression model is represented as a probabilistic timed transition system (PTTS): the state transitions are probabilistic, and, in many cases, are timed, that is, transitions after a given time period. An individual starts from the upper state S (Susceptible). If an individual receives a vaccine, the individual enters a new susceptible state represented by a dotted box. The dashed lines represent state transitions triggered by either interactions with infectious individuals or vaccination. The solid lines represent probabilistic timed state transitions. The shapes with a solid border represent states of an unvaccinated individual; those with a dashed border represent states of a vaccinated individual. The thicker lines represent larger probabilities. Therefore, a vaccinated individual has a smaller probability of getting infected (protection against infection), and, even if infected, the individual has a smaller probability of being hospitalized, needing ventilation, or dying (protection against severe illness).