Linda Rass

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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(More)
Exact results have previously been obtained concerning the spread of infection in continuous space contact models describing a class of multi-type epidemics. Pandemic lower and upper bounds were obtained for the spatial final size. Pandemic results have also been obtained for a discrete space model on the integer lattice using an infinite matrix formulation(More)
Exact results concerning the asymptotic speed of propagation of infection have recently been obtained for the multi-type SIS epidemic in continuous space when the contact distributions are assumed to be symmetric with the Laplace transforms finite for all entries. There is a link between the equations for this epidemic and the equations for a multi-type(More)
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(More)
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.(More)
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(More)
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.(More)
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.
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(More)
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(More)