28,299 research outputs found

    Compartmental analysis of dynamic nuclear medicine data: models and identifiability

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    Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models. The second paper will utilize this framework in order to show how non-linear regularization schemes can be applied to obtain numerical estimates of the tracer coefficients in the case of nuclear medicine data corresponding to brain, liver and kidney physiology

    Products of Compartmental Models in Epidemiology.

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    We show that many structured epidemic models may be described using a straightforward product structure in this paper. Such products, derived from products of directed graphs, may represent useful refinements including geographic and demographic structure, age structure, gender, risk groups, or immunity status. Extension to multistrain dynamics, that is, pathogen heterogeneity, is also shown to be feasible in this framework. Systematic use of such products may aid in model development and exploration, can yield insight, and could form the basis of a systematic approach to numerical structural sensitivity analysis

    Explicit formulas for a continuous stochastic maturation model. Application to anticancer drug pharmacokinetics/pharmacodynamics

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    We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the system output under inhomogeneous killing and when the input follows a time-inhomogeneous Poisson process. This approach allows the discussion of identifiability issues which are of difficult access for finite compartmental models. The article ends up with an example of application for anticancer drug pharmacokinetics/pharmacodynamics.Comment: Revised version, accepted for publication in Stochastic Models (Taylor & Francis

    A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence

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    Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form ÎČIpSq\beta I_p S_q for the case p<1 are constructed. Global stability of the models is thereby established