45 research outputs found
Numerical equilibrium analysis for structured consumer resource models
In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for “Daphnia consuming algae” models in C-code. The results obtained by way of this implementation are shown in the form of graphs
Numerical continuation of equilibria of physiologically structured population models
The paper introduces a new numerical method for continuation of equilibria of models describing physiologically structured populations. To describe such populations, we use integral equations coupled with each other via interaction (or feedback) variables. Additionally we allow interaction with unstructured populations, described by ordinary differential equations. The interaction variables are chosen such that if they are given functions of time, each of the resulting decoupled equations becomes linear. Our numerical procedure to approximate an equilibrium will use heavily this special form of the underlying equations. We also establish a method for local stability analysis of equilibria in dependence on parameters
From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis
Mass-vaccination campaigns are an important strategy in the global fight
against poliomyelitis and measles. The large-scale logistics required for these
mass immunisation campaigns magnifies the need for research into the
effectiveness and optimal deployment of pulse vaccination. In order to better
understand this control strategy, we propose a mathematical model accounting
for the disease dynamics in connected regions, incorporating seasonality,
environmental reservoirs and independent periodic pulse vaccination schedules
in each region. The effective reproduction number, , is defined and proved
to be a global threshold for persistence of the disease. Analytical and
numerical calculations show the importance of synchronising the pulse
vaccinations in connected regions and the timing of the pulses with respect to
the pathogen circulation seasonality. Our results indicate that it may be
crucial for mass-vaccination programs, such as national immunisation days, to
be synchronised across different regions. In addition, simulations show that a
migration imbalance can increase and alter how pulse vaccination should
be optimally distributed among the patches, similar to results found with
constant-rate vaccination. Furthermore, contrary to the case of constant-rate
vaccination, the fraction of environmental transmission affects the value of
when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl
Tunable kinetic proofreading in a model with molecular frustration
In complex systems, feedback loops can build intricate emergent phenomena, so
that a description of the whole system cannot be easily derived from the
properties of the individual parts. Here we propose that inter-molecular
frustration mechanisms can provide non trivial feedback loops which can develop
nontrivial specificity amplification. We show that this mechanism can be seen
as a more general form of a kinetic proofreading mechanism, with an interesting
new property, namely the ability to tune the specificity amplification by
changing the reactants concentrations. This contrasts with the classical
kinetic proofreading mechanism in which specificity is a function of only the
reaction rate constants involved in a chemical pathway. These results are also
interesting because they show that a wide class of frustration models exists
that share the same underlining kinetic proofreading mechanisms, with even
richer properties. These models can find applications in different areas such
as evolutionary biology, immunology and biochemistry