Project 1 - Disease Transmission on Social Networks
Description: Stroeymeyt et al. recently showed that when a pathogen enters an ant colony, contact between ants are modified in order to protect the queen and nurses from receiving a high pathogen load. The project consists in (i) understanding the experiment (which includes the use of technology to track individual ants) as well as the analysis presented in the article, (ii) developing simulations that reproduce the main results of the paper, and (iii) exploring how different contact rules lead to different disease dynamics. The context article provides background information on networks.
Learning outcomes: students will describe creative uses of technology, design and simulate an agent-based model, use networks and outline their properties, and generalize the results of the article to other types of interactions between agents.
Description: Zekri et al. discuss a lattice-based model of fire propagation, where the effect of an heterogeneous distribution of combustible materials, as well as long-distance interactions between burning and non-burning cells are taken into account. The goals of the project are (i) to reproduce the various patterns of fire propagation discussed in the article, and (ii) to explore how fire spreads in different realistic environments (e.g. forests or inhabited areas), which will be defined by the project team. The context article describes experiments on the propagation of vegetation fires, whose findings may be used to estimate model parameters.
Learning outcomes: students will identify the essential elements in a model of fire propagation, use concepts of dynamic phenomena on networks, develop numerical simulations of discrete systems, discuss scalings, compute critical exponents, and extend the use of the model to different situations.
Project 3 - Low-dimensional Modeling of the Immune Response
Description: Mendonça et al. explore the use of a low-dimensional delay dynamical system to describe a complex phenomenon, in this case the immune response. The goals of the project are (i) to learn how low-dimensional models may be useful to describe complex systems and (ii) to understand and reproduce the simulations and linear stability analyses presented in the article.
Learning outcomes: students will describe, simulate, and analyze delay differential equations, and summarize how low-dimensional models may be used to describe the dynamics of complex systems.
Description: This project is based on a 2007 article by J. Legrand et al., which discusses a stochastic model of Ebola infections. The goals are (i) to understand the approach described in the article, (ii) to develop a numerical simulation of the proposed stochastic model, (iii) to calibrate the model on more recent epidemics (examples are shown in the article for previous epidemics), and (iv) to investigate the role of prevention strategies (through changes in model parameter values).
Learning outcomes: students will explain the basic principles of epidemiological modeling, describe and apply the Gillespie algorithm, calibrate their model to data, and use it to assess mitigation strategies.
Context Article: Ebola virus disease: past, present and future, H. Rajak, D.K. Jain, A. Singh, A.K. Sharma, A. Dixit, Asian Pacific Journal of Tropical Biomedicine 5, 337-343 (2015)
Description: In a 2011 article, van den Berge et al. introduced the notion of super-models, which are used to improve the accuracy of simple and thus imperfect models by combining their outputs. This approach is believed to be particularly useful when modeling complex systems. Two context articles discuss applications to climate modeling. The goals of the project are (i) to understand when and why super-models may be useful (starting with the context articles and following up with additional research) and (ii) to reproduce the results of the main article, which illustrates the concept on the Lorenz model.
Learning outcomes: students will explain the origins of the Lorenz system, simulate, and analyze its dynamics, discuss the properties of chaotic systems, describe the use of super-models in complex systems modeling, and apply these concepts to numerical simulations of the Lorenz model.
Description: Popović et al. have devised a simple geometric model to characterize melt ponds in the arctic. The goals of the project are (i) to understand the approach discussed in the article, (ii) to reproduce the model and its results, and (iii) see whether the model applies to deforestation, as described in the context article.
Learning outcomes: Students will demonstrate knowledge of phenomenological modeling, develop associated numerical simulations, discuss scalings, critical phenomena, and fractal dimension, and extend their modeling approach to a different context.