Modeling Exit Strategies from COVID-19 Lockdown with a Focus on Antibody Tests

Reinhard German; Anatoli Djanatliev; Lisa Maile; Peter Bazan; Holger Hackstein

Based on this, a state chart for the progression of the disease from the view of a single person can be defined, it is shown in Fig. 1 and represents an extended SEIR model. Persons are initially susceptible, then exposed after infection, after the latency period a person gets infectious and is recovered or dead afterwards. Persons in recovered are assumed to be immune and cannot be infected again. The state infectious has substates: first there is the state prodromal in which no or only mild symptoms are shown, afterwards there is a split between asymptomatic and symptomatic cases. The symptomatic ones are further split into mild, severe, and critical, the last two of them are again subdivided into sequential states at home, hospitalized, and ICU. We also divide the recovered state into the substates was_asymptomatic and was_symptomatic, a separation which we need for the antibody tests. At each time instance the state chart is in exactly one state, for every (sub-)state without substates either a sojourn time distribution (e.g., latency period in exposed) or an event (e.g., infection by another person in susceptible) for leaving the state must be defined. In case of more than one outgoing arrow of a state, switching probabilities are required. For instance, persons leaving the substates of state infectious have different probabilities to get either back to susceptible (if the person is not immune afterwards, by default this probability is set to zero) or to recovered or dead. All necessary information for such sojourn times and switching probabilities can be obtained from the data mentioned in the previous paragraph. In order to model also aspects like governmental interventions and testing, further attributes are required. Every person has a social status: normal, reduced, and isolated; initial social status is normal. Considered governmental interventions are: