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Global stability for an SEIR epidemiological model with varying infectivity and infinite delay
The relative biologic effectiveness versus linear energy transfer curve as an outputinput relation for linear cellular systems
1.  Department of Radiation Oncology, Stanford University, Stanford, CA 94305, United States 
2.  Department of Mathematics, Colorado State University, Fort Collins, CO 80523, United States 
Here we introduce a differential equation formulation for a signalandsystem model that sees cells as systems, different radiation types as input, and cellular responses as output. Because of scant knowledge of the underlying biochemical network, the current version is necessarily a work in progress. It explains the RBELET curve using not just input parameters but also systems internal state parameters. These systems internal state parameters represent parts of a biochemical network within a cell. Although multiple biochemical parts may well be involved, the shape of the RBELET curve is reproduced when only three system parameters are related to three biochemical parts: the molecular machinery for DNA double strand break repair; the molecular pathways for handling oxidative stress; and the radiolytic products of the cellular water.
Despite being a simplified ''toy model,'' changes in the systems state parameters lead to model curves that are refutable in a modern molecular biology laboratory. As the parts in the biochemical network of the radiation response are being further elucidated, this model can incorporate new systems state parameters to allow a more accurate fit.
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