Current models for determining dementia progression are network diffusion models derived from the heat equation without diffusion sources, and they do not model the disease agents (misfolded β-amyloid and τ -protein) transmission dynamics. In this paper, we derive from a SIRI (Susceptible-Infected-Recovered-Infected) epidemic model a simplified model under the information-centric paradigm over a network of heterogeneous agents and including the long-range dispersal of disease agents. The long-range disease agent dispersal is implemented by including the Mellin and Laplace transforms in the adjacency matrix of the graph network. We analyze the influence of different transforms on the epidemic threshold which shows when a disease dies off. Further we analyze the dynamical properties of this novel model and prove new conditions on the structure of the network and model parameters that distinguish important dynamic regimes such as endemic, epidemic and infection-free. We demonstrate how this model can be used for disease prediction and how control strategies can be developed for disease mitigation.
Brain tumor patients frequently experience tumor-induced alterations in cognitive functions. The early detection of such alterations becomes imperative in the clinical environment and with this the need for computational tools that are capable of quantitatively characterizing functional connectivity changes observed in brain imaging data. This paper presents the application of a novel modern control concept, pinning controllability, to determine intervention points (driver nodes) in the brain tumor-bearing resting-state connectome. The theoretical frameworks provides us with the minimal number of "driver nodes", and their location to determine the full control over the obtained graph network in order to provide a change in the network's dynamics from an initial state (disease) to a desired state (non-disease). Thus we are able to quantify the tumor-induced alterations in different brain regions and the differences in brain connectivity and dynamics. The achieved results will provide clinicians with techniques to identify more tumor-affected regions and biological pathways for brain cancer, to design and test novel therapeutic solutions.
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