ABSTRACT
We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the classical SIR model of Kermack and McKendrick. First, we study the long-time behavior of the solutions and show that there is a "selection via propagation" phenomenon: starting with N strains, only a subset of them - that we identify - propagates and invades space, with some given speeds that we compute. Then, we obtain some qualitative properties concerning the effects of the competition between the different strains on the outcome of the epidemic. In particular, we prove that the dynamics of the model is not characterized by the usual notion of basic reproduction number, which strongly differs from the classical case with one strain.
Subject(s)
Epidemics , Models, Biological , Reproduction , Epidemiological Models , DiffusionABSTRACT
The objective of this study was to evaluate the variations in the degree of conversion (DC) of a light-curing composite resin when the thickness or the translucency of lithium disilicate-enriched glass-ceramic veneers are modified. IPS e. max® CAD blocks of the MT-A2, LT-A2 and MO1 types were cut to obtain four slices with thicknesses ranging from 0.6 mm to 1 mm. A strictly light-curing composite resin (G-aenial Universal Injectable) was injected in the empty part of a silicone mold so that the veneer could then be inserted under digital pressure to the stop. A 40 s light cure (1400 mW/cm2) was then performed. Resin samples were analyzed using Fourier transform infrared (FTIR) spectroscopy. When the degree of translucency of the ceramic was modified, a decrease in the resin conversion rate was noted, but with a non-significant global p-value (p = 0.062). Interestingly, the degree of conversion of the light-curing composite resin was also modified when the ceramic's thickness increased, especially when it was over 1 mm (DC0.6 > DC0.7 > DC0.8 > DC1; p < 0.0001). This confirms that the degree of conversion of a bonding material is very dependent on the ceramic's thickness. Contradictory data are, however, found in the literature, where there are reports of an absence of a difference between the DC obtained with thicknesses of ceramics of 0.7 and 2 mm.
ABSTRACT
We introduce a model designed to account for the influence of a line with fast diffusion-such as a road or another transport network-on the dynamics of a population in an ecological niche.This model consists of a system of coupled reaction-diffusion equations set on domains with different dimensions (line / plane). We first show that, in a stationary climate, the presence of the line is always deleterious and can even lead the population to extinction. Next, we consider the case where the niche is subject to a displacement, representing the effect of a climate change. We find that in such case the line with fast diffusion can help the population to persist. We also study several qualitative properties of this system. The analysis is based on a notion of generalized principal eigenvalue developed and studied by the authors (2019).
