Title: Deterministic Epidemic Models for Metapopulation Networks: Infection by Transportation and the Poincare-Hopf Theorem

Abstract: Mathematical models of epidemics are important for understanding how infectious diseases spread among populations, and whether the disease will eventually die out. This talk will introduce an SIS (Susceptible-Infected-Susceptible) model for the spreading of a disease as infected individuals travel across a network where each node represents a large population. A real-world example is the 2003 SARS virus spreading across cities around the world via air travel. A necessary and sufficient condition for the disease to eventually die out is obtained, and if the condition is not satisfied, we show that the network converges to a unique diseased state.

Last, I introduce the Poincare-Hopf Theorem as a tool from differential topology, which allows the drawing of powerful conclusions for generalised versions of the epidemic model. An important problem is to develop controllers for the network, e.g. by controlling the recovery rate of each population, to eventually eliminate the disease. An impossibility result is obtain, showing that a large class of feedback controllers will fail to eliminate the disease if the uncontrolled network itself cannot reach the disease-free state.

Bio: Mengbin Ye was born in Guangzhou, China. He received the B.E. degree (with First Class Honours) in mechanical engineering from the University of Auckland, Auckland, New Zealand in 2013, and the Ph.D. degree in engineering at the Australian National University, Canberra, Australia in 2018. He is currently a postdoctoral researcher with the Faculty of Science and Engineering, University of Groningen, Netherlands.
  
He has been awarded the 2018 Springer PhD Thesis Prize, and was Highly Commended in the Best Student Paper Award at the 2016 Australian Control Conference. His current research interests include opinion dynamics and decision-marking networks, epidemic network modelling, consensus and synchronisation of multi-agent systems, and localisation using bearing measurements.