3,496 research outputs found
Explicit formulas for a continuous stochastic maturation model. Application to anticancer drug pharmacokinetics/pharmacodynamics
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 Compartmental Model for Traffic Networks and its Dynamical Behavior
We propose a macroscopic traffic network flow model suitable for analysis as
a dynamical system, and we qualitatively analyze equilibrium flows as well as
convergence. Flows at a junction are determined by downstream supply of
capacity as well as upstream demand of traffic wishing to flow through the
junction. This approach is rooted in the celebrated Cell Transmission Model for
freeway traffic flow. Unlike related results which rely on certain system
cooperativity properties, our model generally does not possess these
properties. We show that the lack of cooperativity is in fact a useful feature
that allows traffic control methods, such as ramp metering, to be effective.
Finally, we leverage the results of the paper to develop a linear program for
optimal ramp metering
Modelling prevention strategies in Public Health
Various schemes of prevention measures in public health are developed and analyzed on the basis of a general mathematical model. Features related to cost issues,
including primary and secondary prevention interventions, differential survival experiences and communicable diseases are in turn used to show the potentialities of
the theoretical framework. Statistical estimation procedures are briefly discussed and a numerical application is presented with reference to Italian cancer data
The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies
This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of this protection, and that age related empirical data are likely to be most appropriate for estimating these characteristics
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