We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
In this paper we propose a discrete criss-cross model of tuberculosis (TB) transmission in a heterogeneous population, which consists of two different subpopulations: homeless and non-homeless people. This criss-cross model is based on the simple continuous SIS model with bilinear transmission function and constant inflow into both subpopulations considered previously by us. We make preliminary stability analysis. We show that to control the spread of the infectious disease in a heterogeneous population...
Blood vessel sprouting (angiogenesis) is one of the hallmarks of cancer. Better quantitative understanding of this process would allow more effective antiangiogenic therapies to be developed. It has been hypothesised that not only the number of endothelial cells, but also the quality of the vasculature play an important role in how chemo- and radiotherapies are delivered to tumour site. Hence in this study a minimally-parametrised mathematical model of endothelial cell proliferation and maturation...
We have investigated the behaviour of solutions of elliptic quasi-linear problems in a neighbourhood of boundary singularities in bounded and unbounded domains. We found exponents of the solution’s decreasing rate near the boundary singularities.
Antiviral therapy for HIV-infected patients has greatly improved in recent years. Administration of drug combinations consisting of two or more different drugs can reduce and maintain virus load below detection level in many patients. Cyclic administration of the immune activator interleukin-2 (IL-2) in combination with highly active antiretroviral therapy (HAART) has been suggested as an effective strategy to realize long-term control of HIV replication in vivo. In this article, we formulate a...
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