Reaction-diffusion models in weighted and directed connectomes.

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional phenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our precise connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances. Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway. In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation was realized in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

Agent-based modeling to estimate the impact of lockdown scenarios and events on a pandemic exemplified on SARS-CoV-2.

In actual pandemic situations like COVID-19, it is important to understand the influence of single mitigation measures as well as combinations to create most dynamic impact for lockdown scenarios. Therefore we created an agent-based model (ABM) to simulate the spread of SARS-CoV-2 in an abstract city model with several types of places and agents. In comparison to infection numbers in Germany our ABM could be shown to behave similarly during the first wave. In our model, we implemented the possibility to test the effectiveness of mitigation measures and lockdown scenarios on the course of the pandemic. In this context, we focused on parameters of local events as possible mitigation measures and ran simulations, including varying size, duration, frequency and the proportion of events. The majority of changes to single event parameters, with the exception of frequency, showed only a small influence on the overall course of the pandemic. By applying different lockdown scenarios in our simulations, we could observe drastic changes in the number of infections per day. Depending on the lockdown strategy, we even observed a delayed peak in infection numbers of the second wave. As an advantage of the developed ABM, it is possible to analyze the individual risk of single agents during the pandemic. In contrast to standard or adjusted ODEs, we observed a 21% (with masks) / 48% (without masks) increased risk for single reappearing participants on local events, with a linearly increasing risk based on the length of the events.