Complex Networks: Development of a three particle reaction-diffusion model on a complex network.

Abstract

This master thesis couples endemic modeling of diseases with complex networks and diffusion. Previous established models are visited and results for these are reproduced. The goal of this thesis was to expand upon these models and create a more powerful tool for modeling the outbreak of diseases. Coupled with networks, this creates a new powerful model with similarities to the real world behaviour of disease spreading.Both analytical and numerical studies have been made. The main work in this thesis has been developing a computational framework in which to run simulations on the new and old models. The end result is an efficient computer program designed to be flexible and user friendly. The flexibility of the program enabled us to quickly make alterations to the model and study the results. Code for generating plots also made it possible to quickly study the results of a simulation. By making it easy to change the code we hope that others might find it useful in further study.The analytically derived steady state solutions follow the numerical simulations quite well. The knowledge that approximations in the analytical solutions were negligible made it possible to draw general conclusions using these mathematical results.