Analysis of threshold-type behaviour in mathematical models of the intrusion of a novel macroparasite in a host colony.

Macroparasites include worms, ticks, mites, bugs and fleas. These parasites are well known to induce morbidity effects including a reduction in the hosts' reproductive output and survival. An important scenario is the introduction of a new macroparasite into an established host population which may be caused by the climate change and by the transport of domestic animals. The aim of the article is to demonstrate an interesting feature of this scenario using a mathematical model with four dimensionless parameters. Six possible scenarios of introducing a new macroparasite into a host colony, ranging from the elimination of the new pathogen, through guaranteed host and parasite coexistence, to the collapse of the host colony are distinguished. The threshold surfaces in the space of parameters which separate the different scenarios are found. Some special limit cases are discussed.

A profile analysis of propagating calcium waves.

The identity of the wave messenger mediating the propagation of intracellular Ca2+ waves in a variety of cells is currently controversial. There is disagreement as to whether the observed waves are mediated by the diffusion of Ca2+ or by the diffusion of inositol 1,4,5-trisphosphate. Resolution of this question will help to elucidate the mechanisms underlying intracellular Ca2+ waves and oscillations. It has been suggested that the diffusion coefficient of the wave messenger, D, may be evaluated by means of the profile equation, D = c lambda, where c is the wave speed, and lambda is the space constant of the wave front. We show that this equation is not, in general, correct. We derive a more comprehensive form of the profile equation, including the effect of buffering of the wave messenger, and show that the profile equation may be used to estimate the diffusion coefficient of the wave messenger only if the details of the reaction and buffering kinetics are known.