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Atherosclerosis, hardening of the arteries, originates from small plaques in the arteries; it is a major cause of disability and premature death in the United States and worldwide. In this paper, we study the bifurcation of a highly nonlinear and highly coupled PDE model describing the growth of an arterial plaque in the early stage of atherosclerosis. The model involves LDL and HDL cholesterols, macrophage cells, and foam cells, with the interface separating the plaque and blood flow regions being a free boundary. We establish finite branches of symmetry-breaking stationary solutions which bifurcate from the radially symmetric solution. Since plaques in reality are unlikely to be strictly radially symmetric, our result would be useful to explain the asymmetric shapes of plaques. [ABSTRACT FROM AUTHOR]

In a recent work [1] , a mathematical model is derived to explore the role that the white-tail deer plays in the geographic spread of the black-legged tick Ixodes scapularis in the northeast of the United States of America. The threshold dynamics is rigorously investigated in terms of the basic reproduction number, for the cases of the 1-D whole space Ω = R and general bounded spatial domain Ω with homogeneous Neumann and Direchlet boundary conditions. However, the minimal wave speed and spread speed of the model, which are the motivation of this model and thus most important, are only explored numerically. In the present paper, we offer a rigorous theoretical confirmation of what are numerically observed in [1] , concluding that if the basic reproduction number is larger than one, the model allows a spread speed which is also the minimal speed of traveling wave fronts, and this speed is linearly deterministic. [ABSTRACT FROM AUTHOR]