Biomedical subjects

L M Sander

Publications and source records attributed to L M Sander.

4 recordsLinked to original sources

PubMed2004

SIS epidemics with household structure: the self-consistent field method.

We consider a stochastic SIS infection model for a population partitioned into m households assuming random mixing. We solve the model in the limit m --> infinity by using the self-consistent field method of statistical physics. We derive a number of explicit results, and give numerical illustrations. We then do numerical simulations of the model for finite m and without random mixing. We find in many of these cases that the self-consistent field method is a very good approximation.

Endemic Diseases↗

PubMed2002

Geography in a scale-free network model.

We offer an example of a network model with a power-law degree distribution, P(k) approximately k(-alpha), for nodes, but which nevertheless has a well-defined geography and a nonzero threshold percolation probability for alpha>2, the range of real-world contact networks. This is different from p(c)=0 for alpha<3 results for the original well-mixed scale-free networks. In our lattice-based scale-free network, individuals link to nearby neighbors on a lattice. Even considerable additional small-world links do not change our conclusion of nonzero thresholds. When applied to disease propagation, these results suggest that random immunization may be more successful in controlling human epidemics than previously suggested if there is geographical clustering.

Journal Article↗

PubMed2001

Fluctuation effects in an epidemic model.

We study a discrete epidemic model A+B-->2A in one and two dimensions (1D and 2D). In 1D for low concentration theta, we find that a depletion zone exists ahead of the front and the average velocity of the front approaches v=theta/2. In the 1D high concentration limit, we find that the velocity approaches v=1-e(-theta/2). In 2D, for low concentration we also find a depletion zone, and the velocity scales as v approximately theta(0.6), which is different from the scaling expected from the mean field approximation, v approximately theta(0.5). Analysis of the interface width scaling properties demonstrated that the front dynamics of this reaction are not governed by the Kardar-Parisi-Zhang equation.

Journal Article↗

PubMedDate not supplied

Percolation on heterogeneous networks as a model for epidemics.

We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong heterogeneity, i.e. a wide range of variation of susceptibility, patchiness in the spread of the epidemic is very likely, and the criterion for epidemic outbreak depends strongly on the heterogeneity. These results are qualitatively different from those of standard models in epidemiology, but correspond to real effects. We suggest that heterogeneity in the epidemic will affect the phylogenetic distance distribution of the disease-causing organisms. We also investigate small world lattices, and show that the effects mentioned above are even stronger.

Disease Outbreaks↗