Biomedical subjects

L Rass

Publications and source records attributed to L Rass.

8 recordsLinked to original sources

PubMed1999

The derivation of certain pandemic bounds.

Exact results have previously been obtained concerning the spread of infection in continuous space contact models describing a class of multitype epidemics. The Pandemic Theorem gave a lower bound for the spatial final size. A discrete space model is considered. A simpler, more direct proof based on an infinite matrix formulation of the final size equations is used to obtain the pandemic result for this model. An upper bound is obtained, which is valid for both continuous and discrete space models. This enables a limiting result to be obtained for the spatial final size when the amount of initial infection tends to zero.

Epidemiology↗

PubMed1999

Strategic and genetic models of evolution.

A new model which allows both for the effect of behavioural patterns on productive matings and for parental investment in the survival of offspring to maturity is considered. This combines ideas from genetics and evolutionary game theory, and provides a more realistic formulation to describe mating behaviour than the traditional 'battle of the sexes' model. Allowing individuals to migrate leads to spatial versions of both models. The saddle point method is used to obtain the speed of first spread of new genes/strategies in both spatial systems.

Biological Evolution↗

PubMed1998

Spatial Mendelian games.

This paper considers complex models arising in sociobiology. These combine genetic and strategic aspects to model the effect of gene-linked strategies on the ability of individuals to survive to maturity, mate and produce offspring. Several important models considered in the literature are generalised and extended to incorporate a spatial aspect. Individuals are allowed to migrate. Contests, e.g. for food or amongst males for females, take place locally. The choice of the point at which the population structure is measured affects the complexity of the equations describing the system, although it is possible to utilise any point in the life cycle. For our spatial models the simplest approach is to measure the population structure immediately after migration. A saddle point method, developed by the authors, has previously been used to obtain results for simple discrete time spatial models. It is utilised here to obtain the speed of first spread of a new gene-linked strategy for the much more complex sociobiological models included in this paper. This demonstrates the wide-ranging applicability and power of the method.

Alleles↗

PubMed1997

Discrete time spatial models arising in genetics, evolutionary game theory, and branching processes.

A saddle point method is used to obtain the speed of first spread of new genotypes in genetic models and of new strategies in game theoretic models. It is also used to obtain the speed of the forward tail of the distribution of farthest spread for branching process models. The technique is applicable to a wide range of models. They include multiple allele and sex-linked models in genetics, multistrategy and bimatrix evolutionary games, and multitype and demographic branching processes. The speed of propagation has been obtained for genetics models (in simple cases only) by Weinberger and Lui, using exact analytical methods. The exact results were obtained only for two-allele, single-locus genetic models. The saddle point method agrees in these very simple cases with the results obtained by using the exact analytic methods. Of course, it can also be used in much more general situations far less tractable to exact analysis. The connection between genetic and game theoretic models is also briefly considered, as is the extent to which the exact analytic methods yield results for simple models in game theory.

Alleles↗

PubMed1986

The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic.

A model has been formulated in to describe the spatial spread of an epidemic involving n types of individuals, when triggered by the introduction of infectives from outside. Wave solutions for such a model have been investigated in and have been shown only to exist at certain speeds. This paper establishes that the asymptotic speed of propagation, as defined in Aronson and Weinberger, of such an epidemic is in fact c0, the minimum speed at which wave solutions exist. This extends the known result for the one-type and host-vector epidemics.

Biometry↗

PubMed1984

The uniqueness of wave solutions for the deterministic non-reducible n-type epidemic.

In a recent paper, [8], we investigated the existence of wave solutions for a model of the deterministic non-reducible n-type epidemic. In this paper we first prove two properties left as an open question in that paper. The uniqueness of the wave solutions at all speeds for which a wave solution exists is then established. Only an exceptional case is not covered.

Disease Outbreaks↗

PubMed1984

The spatial spread and final size of the deterministic non-reducible n-type epidemic.

A model has been formulated in [6] to describe the spatial spread of an epidemic involving n types of individual, and the possible wave solutions at different speeds were investigated. The final size and pandemic theorems are now established for such an epidemic. The results are relevant to the measles, host-vector, carrier-borne epidemics, rabies and diseases involving an intermediate host. Diseases in which some of the population is vaccinated, and models that divide the population into several strata are also covered.

Animals↗

PubMed1983

Wave solutions for the deterministic non-reducible n-type epidemic.

A model is formulated to describe the spatial spread of an epidemic involving n types of individual. This encompasses the measles, host-vector and carrier-borne epidemics, and in addition rabies involving several species of animal. The existence, uniqueness and non-existence of wave solutions for different speeds are established for this model.

Animals↗