15,273 research outputs found
On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems
Delays in biological systems may be used to model events for which the
underlying dynamics cannot be precisely observed. Mathematical modeling of
biological systems with delays is usually based on Delay Differential Equations
(DDEs), a kind of differential equations in which the derivative of the unknown
function at a certain time is given in terms of the values of the function at
previous times. In the literature, delay stochastic simulation algorithms have
been proposed. These algorithms follow a "delay as duration" approach, namely
they are based on an interpretation of a delay as the elapsing time between the
start and the termination of a chemical reaction. This interpretation is not
suitable for some classes of biological systems in which species involved in a
delayed interaction can be involved at the same time in other interactions. We
show on a DDE model of tumor growth that the delay as duration approach for
stochastic simulation is not precise, and we propose a simulation algorithm
based on a ``purely delayed'' interpretation of delays which provides better
results on the considered model
Epidemics on contact networks: a general stochastic approach
Dynamics on networks is considered from the perspective of Markov stochastic
processes. We partially describe the state of the system through network motifs
and infer any missing data using the available information. This versatile
approach is especially well adapted for modelling spreading processes and/or
population dynamics. In particular, the generality of our systematic framework
and the fact that its assumptions are explicitly stated suggests that it could
be used as a common ground for comparing existing epidemics models too complex
for direct comparison, such as agent-based computer simulations. We provide
many examples for the special cases of susceptible-infectious-susceptible (SIS)
and susceptible-infectious-removed (SIR) dynamics (e.g., epidemics propagation)
and we observe multiple situations where accurate results may be obtained at
low computational cost. Our perspective reveals a subtle balance between the
complex requirements of a realistic model and its basic assumptions.Comment: Main document: 16 pages, 7 figures. Electronic Supplementary Material
(included): 6 pages, 1 tabl
Modeling biological systems with delays in Bio-PEPA
Delays in biological systems may be used to model events for which the
underlying dynamics cannot be precisely observed, or to provide abstraction of
some behavior of the system resulting more compact models. In this paper we
enrich the stochastic process algebra Bio-PEPA, with the possibility of
assigning delays to actions, yielding a new non-Markovian process algebra:
Bio-PEPAd. This is a conservative extension meaning that the original syntax of
Bio-PEPA is retained and the delay specification which can now be associated
with actions may be added to existing Bio-PEPA models. The semantics of the
firing of the actions with delays is the delay-as-duration approach, earlier
presented in papers on the stochastic simulation of biological systems with
delays. These semantics of the algebra are given in the Starting-Terminating
style, meaning that the state and the completion of an action are observed as
two separate events, as required by delays. Furthermore we outline how to
perform stochastic simulation of Bio-PEPAd systems and how to automatically
translate a Bio-PEPAd system into a set of Delay Differential Equations, the
deterministic framework for modeling of biological systems with delays. We end
the paper with two example models of biological systems with delays to
illustrate the approach.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005
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