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Biomedical subjects

J Grasman

Publications and source records attributed to J Grasman.

8 recordsLinked to original sources
PubMed2003

The multifractal structure of arterial trees.

Fractal properties of arterial trees are analysed using the cascade model of turbulence theory. It is shown that the branching process leads to a non-uniform structure at the micro-level meaning that blood supply to the tissue varies in space. From the model it is concluded that, depending on the branching parameter, vessels of a specific size contribute dominantly to the blood supply of tissue. The corresponding tissue elements form a dense set in the tissue. Furthermore, if blood flow in vessels can get obstructed with some probability, the above set of tissue elements may not be dense anymore. Then there is the risk that, spread out over the tissue, nutrient and gas exchange fall short.

Animals↗
PubMed2001

Mathematical conservation ecology: a one-predator-two-prey system as case study.

A method is presented to analyse the long-term stochastic dynamics of a biological population that is at risk of extinction. From the full ecosystem the method extracts the minimal information to describe the long-term dynamics of that population by a stochastic logistic system. The method is applied to a one-predator-two-prey model. The choice of this example is motivated by a study on the near-extinction of a porcupine population by mountain lions whose presence is facilitated by mule deer taking advantage of a change in land use. The risk of extinction is quantified by the expected time of extinction of the population.

Animals↗
PubMed2001

A two-component model of host-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control.

A two-component differential equation model is formulated for a host-parasitoid interaction. Transient dynamics and population crashes of this system are analysed using differential inequalities. Two different cases can be distinguished: either the intrinsic growth rate of the host population is smaller than the maximum growth rate of the parasitoid or vice versa. In the latter case, the initial ratio of parasitoids to hosts should exceed a given threshold, in order to (temporarily) halt the growth of the host population. When not only oviposition but also host-feeding occurs the dynamics do not change qualitatively. In the case that the maximum growth rate of the parasitoid population is smaller than the intrinsic growth rate of the host, a threshold still exists for the number of parasitoids in an inundative release in order to limit the growth of the host population. The size of an inundative release of parasitoids, which is necessary to keep the host population below a certain level, can be determined from the two-component model. When parameter values for hosts and parasitoids are known, an effective control of pests can be found. First it is determined whether the parasitoids are able to suppress their hosts fully. Moreover, using our simple rule of thumb it can be assessed whether suppression is also possible when the relative growth rate of the host population exceeds that of the parasitoid population. With a numerical investigation of our simple system the design of parasitoid release strategies for specific situations can be computed.

Animals↗
PubMed1998

Stochastic epidemics: the expected duration of the endemic period in higher dimensional models.

A method is presented to approximate the long-term stochastic dynamics of an epidemic modelled by state variables denoting the various classes of the population such as in SIR and SEIR model. The modelling includes epidemics in populations at different locations with migration between these populations. A logistic stochastic process for the total infectious population is formulated; it fits the long-term stochastic behaviour of the total infectious population in the full model. A good approximation is obtained if only the dynamics near the equilibria is fit.

Citrus↗
PubMed1995

Stochastic epidemics: major outbreaks and the duration of the endemic period.

A study is made of a two-dimensional stochastic system that models the spread of an infectious disease in a population. An asymptotic expression is derived for the probability that a major outbreak of the disease will occur in case the number of infectives is small. For the case that a major outbreak has occurred, an asymptotic approximation is derived for the expected time that the disease is in the population. The analytical expressions are obtained by asymptotically solving Dirichlet problems based on the Fokker-Planck equation for the stochastic system. Results of numerical calculations for the analytical expressions are compared with simulation results.

Communicable Diseases↗
PubMed1994

Reconstruction of the seasonally varying contact rate for measles.

With the extended Kalman filter the time dependent contact rate for measles in the SEIR-model is reconstructed from data of the incidence of this infectious disease in the city of New York. It is concluded that although these data show through the years an irregular change in the number of infected children the contact rate is definitely periodic and follows the season. The analysis gives improved values of the parameters in the SEIR-model for this special problem.

Child↗
PubMed1990

A deterministic model of the cell cycle.

The variability of the duration of the cell cycle is explained by the phenomenon of sensitive dependence upon initial conditions; as may occur in deterministic non-linear systems. Chaotic dynamics of a system is the result of this sensitive dependence. First a deterministic system is formulated that is equivalent to the Smith-Martin transition probability model of the cell cycle. Next the model is extended to a dynamic process that ranges over the cell generations. A deterministic non-linear relationship between the cycle time of the mother and daughter cell is established. It clarifies the variability of mother-daughter correlation for the different cell types. The model is fitted to two different cell cultures; it shows that the graph of the non-linear relation has the same shape for different cell types.

Animals↗