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Seminar WS 23/24 Graduate Seminar on Numerical Simulation

Mathematical Modeling of Infectious Diseases

Offered by
Dr. Martin J. Kühn

Tuesdays: 16-18, room 2.041, Friedrich-Hirzebruch-Allee 7.

Preliminary meeting: 4 July 2023, 16:00, room 2.035, Friedrich-Hirzebruch-Allee 7.

The Sars-CoV-2 pandemic has shown drastically how human society can be impacted by infectious diseases and climate change will accelerate the frequency of dangerous epidemics and pandemics. For newly emerging viruses, nonpharmaceutical interventions (NPIs) have to be implemented until pharmaceutical interventions are available. In order to find the right interventions, future developments of the virus dynamics have to be 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 contact behavior and 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.

To overcome certain limitations of simple models, different extensions can be considered. In order to account for important features of virus dynamics, age stratification can be realized in a straightforward way. To avoid homogeneous mixing in all locations, a hybrid graph-ODE approach could be introduced. Extensions of ODE-based models to Integro-differential equations allow for more realistic infection dynamics. For different models, numerical solution procedures need to be considered.