Controlling Diffusion on Multi-Pathway Spatial Networks: Application to Biological Invasions

An important challenge in agriculture and food security is the control of invasive alien species (IAS) spread that affect important agricultural crops. However, optimal control of such epidemics is a challenging problem. In this thesis, we consider the problem of controlling a multi-pathway epidemiological process on a temporal network. Our focus is on the problem of group-scale interventions, where the objective is to find an optimal set of regions (or groups of nodes) to intervene at so as to minimize the spread. Such interventions correspond to region-wide management techniques, which are more realistic compared to targeted interventions that are typically studied in network science. In this collaborative work, we designed, implemented and analyzed an algorithm called SPREADBLOCKING for intervention problem. Our method uses sample average approximation technique and a linear relaxation of an integer linear program.
This thesis contributes to the implementation of the simulator, experimental framework and analysis. We implemented the multipathway simulator using vectorization methods, and achieved an order of magnitude speed improvement over the previous version. We integrated the simulator with the intervention algorithm. This involved representing simulation instances, which correspond to Susceptible-Exposed-Infectious (SEI) process on the input network to a Susceptible-Infectious-Recovered (SIR) process on a time-expanded graph. For experimental evaluation of the SPREADBLOCKING algorithm, we implemented popular baselines for comparison of our results. Finally, we conducted experiments to evaluate our intervention algorithm on several real-world networks with respect to budget, introduction scenarios and intervention delays.
Our results show superior performance across model parameters compared to the baselines. We note that early discovery of the IAS and speed of intervention are critical to identify intervention candidates under model uncertainty. We observe that groups with high inflow, even though vulnerable, are not necessarily chosen as candidates for intervention. Across model parameters, we note that performance of group-scale interventions is comparable to individual-based interventions in performance, though the former is more practical from an implementation perspective.