Faculty Contact: Francesco Bullo
Abstract: In this work we investigate a class of deterministic models on the propagation of infectious diseases over contact networks with arbitrary topologies. We present a comprehensive review and analysis of equilibria, stability properties, convergence, monotonicity, positivity, and threshold conditions. Our analysis is based on the fundamental properties of non-negative matrices and dynamical systems. Specific contributions for network SI include introducing a deterministic model and presenting its convergence, stability, equilibria, and positivity properties. Regarding network SIS, we review a deterministic model and present alternative proofs for its properties. We also provide an improved iterative algorithm with convergence guarantees to predict the fraction of individuals in the endemic state for this model.
Finally, for the SIR model we propose new results for transient behavior, threshold conditions, stability properties, and asymptotic convergence which are analogous to the scalar case. Our propositions overcome the shortcomings of the previous works and are reinforced by simulations.
- Spring 2016: Shadi Mohagheghi