Infectious diseases continue to pose a significant threat to the health of humans globally. While the spread of pathogens transcends geographical boundaries, the management of infectious diseases typically occurs within distinct spatial units, determined by geopolitical boundaries. The allocation of management resources within and across regions (the "governance structure") can affect epidemiological outcomes considerably, and policy-makers are often confronted with a choice between applying control measures uniformly or differentially across regions. Here, we investigate the extent to which uniform and non-uniform governance structures affect the costs of an infectious disease outbreak in two-patch systems using an optimal control framework. A uniform policy implements control measures with the same time varying rate functions across both patches, while these measures are allowed to differ between the patches in a non-uniform policy. We compare results from two systems of differential equations representing transmission of cholera and Ebola, respectively, to understand the interplay between transmission mode, governance structure and the optimal control of outbreaks. In our case studies, the governance structure has a meaningful impact on the allocation of resources and burden of cases, although the difference in total costs is minimal. Understanding how governance structure affects both the optimal control functions and epidemiological outcomes is crucial for the effective management of infectious diseases going forward.

We show that Nachman's integral equations for the Calderon problem, derived for conductivities in W-2,W-p(Omega), still hold for L-infinity conductivities which are 1 in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of L-infinity conductivities. We rely on Astala-Paivarinta's formulation of the Calderon problem for a framework in which these convergence results make sense.