Mathematical modeling of infectious diseases

Kurzfassung

The Sars-CoV-2 pandemic has shown how humans and human society is impacted by infectious diseases. Until full vaccination of the populations or the right medicine is available, nonpharmaceutical interventions (NPIs) have to be implemented. In order to find the right interventions, the future developments of the virus dynamics have to estimated under different assumptions. A straightforward approach is to use numerical simulation of mathematical models in epidemiology. Mathematical models in epidemiology can be classified according to different categories, e.g., deterministic and stochastic, population-based and agent-based, or endemic and epidemic. While agent-based methods model individual behavior and natural transmission chains in a natural way, classical ODE models are subpopulation-based and hide important features such as mobility or superspreading events behind averaged effects. These models are, on the other hand, computationally much less demanding, and allow for an on-time simulation of many different model scenarios.