Modeling disease agents transmission dynamics in dementia on heterogeneous spatially embedded networks

Abstract

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.