An epidemiological diffusion framework for vehicular messaging in general transportation networks

Countering the potential re-emergence of a deadly infectious disease - information warfare, identifying strategic threats, launching countermeasures

“…A joint investigation of infectious disease and opinion dynamics in presence of spatial hetero-geneity inevitably leads to a computationally complex model with 1) a multiplicity of states representing a combination of stages of the disease, immunocompetency, and cooperativity, and 2) a multiplicity of state transitions representing interactional transitions due to spread of the disease and opinions, non-interactional transitions due to mobility of individuals and the natural progression of the disease in infected individuals. We model these by adapting the metapopulation epidemiological model [6, 9, 12, 23] which relies on a set of differential equations (co-authors of this work have utilized the metapopulation model as well [12, 23]). Metapopulation models have some distinct advantages in modeling the spread of infectious diseases.…”

“…Note that interactions always involve two individuals, hence interactional transitions are represented by quadratic terms; in contrast, the non-interactional transitions involve only one individual and are therefore represented by linear terms. This is typical of epidemiological models starting from the classical Kermack–McKendrick formulation [22]) and onward to the metapopulation models [6, 9, 12, 23]. Our work differs from the metapopulation epidemiological models in that it has additional quadratic terms representing the interactional transitions due to the spread of opinions, and additional linear terms representing preemption due to application of countermeasures.…”

“…Nevertheless, through an application of the strong law of large numbers , under some commonly made regularity assumptions on the stochastic evolutions, one can show that as the number of individuals increases, the fractions of individuals in different system states in the stochastic system converge to the solutions of the CEDE, and the convergence becomes exact in the limit that the number of individuals is infinity. For the mathematical proof we refer to a recent work by one of the co-authors involving the application of the CEDE in a different domain [23]. Thus the CEDE approximates the stochastic process better as the number of individuals increase.…”

“…Each variable in the CEDE represents the fraction of the population who are in a particular system state, each state representing the combination of the cluster inhabited, the stage of the disease, immunocompetency, and cooperativity. Each [22]) and onward to the metapopulation models [6,9,12,23]. Our work differs from the metapopulation epidemiological models in that it has additional quadratic terms representing the interactional transitions due to the spread of opinions, and additional linear terms representing preemption due to application of countermeasures.…”

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“…the disease and opinions, non-interactional transitions due to mobility of individuals and the natural progression of the disease in infectious individuals. We model these by adapting the metapopulation epidemiological model [29,30] which relies on a set of differential equations (co-authors of this work have utilized the metapopulation model as well [33,34]). Metapopulation models have some distinct advantages in modeling the spread of infectious diseases.…”