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

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

In order to find strategies to defeat the pandemic, epidemiological models are used to support decision making. In general, there are two main modeling approaches: an aggregate view based on a system of differential equations, also known as System Dynamics (SD) and an individual-based simulation, also known as Agent-Based Simulation (ABS) [4] . SD models can describe dynamics on an abstract level, people in certain states are represented by their number and for the solution just an ordinary system of differential equations needs to be solved. Standard solvers are available, the size of the system is normally quite small (up to a few ten equations) and a fast, immediate response is possible. In ABS, each individual is modeled explicitly allowing for stochastic and more detailed behavior, underlying is however discrete-event simulation causing higher computational costs (note that also repetitions of the simulations are needed in order to get statistically reliable results). Depending on the goals a suitable modeling approach can be selected. It is also possible to combine both, as an example of hybrid simulation, which has already been applied successfully in healthcare simulations [5] . It should be noted that an SD model corresponds to an ABS where all agents are represented by a Markov chain with the same states as the SD model and the number of agents is taken to infinity [4] . Therefore, all timing in SD is implicitly exponentially distributed. By splitting the SD variables it is also possible to represent phase type distributions such as the Erlang distribution which is less variant [6] . This allows for more realism in SD models. Most models extend well-known SEIR models [7, 8] with the states susceptible, exposed (infected but not yet infectious), infectious, and recovered. In SD models each equation describes the change of the number of people in theses states and in ABS each agent has these internal states.