**Samuel V. Scarpino**

### LECTURE: Towards a Complex Systems Theory of Outbreaks

Infectious disease outbreaks recapitulate biology: they emerge from the multi-level interaction of hosts, pathogens, and their shared environment. As a result, predicting when and where diseases will spread requires a complex systems approach to modeling. In this talk, I will present two examples of how taking such an integrative approach to the science of outbreaks has improved both our understanding of disease and also our public health capacity to intervene. Building from these examples, I will discuss recent work on measureing the intrinsic predictability of diseases. To investigate the question of outbreak prediction, we studied the information theoretic limits to forecasting across a broad set of infectious diseases using permutation entropy as a model independent measure of predictability. Studying the predictability of a diverse collection of historical outbreaks–including, chlamydia, gonorrhea, hepatitis A, influenza, Zika, measles, polio, whooping cough, and mumps–we identify a fundamental entropy barrier for infectious disease time series forecasting. However, we find that for most diseases this barrier to prediction is often well beyond the time scale of single outbreaks, implying prediction is likely to succeed. We also find that the forecast horizon varies by disease and demonstrate that both shifting model structures and social network heterogeneity are the most likely mechanisms for the observed differences in predictability across contagions.

**LECTURE: Why do we cooperate with each other? – from theory to experiment and back**

The emergence of cooperation in societies is one of the most important unanswered questions in science at the moment. Numerous theoretical explanations based in Game Theory have been offered and in the last 10 years a number of experimental works started to be show up to test these theories. Here, I will introduce the basic concepts from game theory, which is used to analyse this problem. Then I go over a number of experiments developed to test different possible mechanisms and the insight it gave us for the further development of the theoretical work.

## **Filippo Radicchi**

**LECTURE: Percolation on complex Networks**

Percolation is one of the most studied models in statistical physics.

It describes how the connectedness at the macroscopic level changes in relation with the microscopic connectivity of the individual elements in a system. Percolation models have been used to study properties of materials, such as porosity and conductivity. In network science, percolation models turned out to be very useful in the analysis of spreading phenomena in social environments, and in robustness studies of technological and infrastructural systems. In this lecture, I will review the state-of-the-art in the study of percolation models in complex networks, including recent developments towards a theoretical description of percolation processes in real-world networks.