Permanence of a delayed SIR epidemic model with density dependent birth rate

AbstractIn this paper, we consider the permanence of a modified delayed SIR epidemic model with density dependent birth rate which is proposed in [M. Song, W. Ma, Asymptotic properties of a revised SIR epidemic model with density dependent birth rate and time delay, Dynamic of Continuous, Discrete and Impulsive Systems, 13 (2006) 199–208]. It is shown that global dynamic property of the modified delayed SIR epidemic model is very similar as that of the model in [W. Ma, Y. Takeuchi, T. Hara, E. Beretta, Permanence of an SIR epidemic model with distributed time delays, Tohoku Math. J. 54 (2002) 581–591; W. Ma, M. Song, Y. Takeuchi, Global stability of an SIR epidemic model with time delay, Appl. Math. Lett. 17 (2004) 1141–1145]

Stability of a mathematical model of tumour-induced angiogenesis

A model consisting of three differential equations to simulate the interactions between cancer cells, the angiogenic factors and endothelial progenitor cells in tumor growth is developed. Firstly, the global existence, nonnegativity and boundedness of the solutions are discussed. Secondly, by analyzing the corresponding characteristic equations, the local stability of three boundary equilibria and the angiogenesis equilibrium of the model is discussed, respectively. We further consider global asymptotic stability of the boundary equilibria and the angiogenesis equilibrium by using the well-known Liapunov–LaSalle invariance principal. Finally, some numerical simulations are given to support the theoretical results

Dynamical Models of Biology and Medicine

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicin

Analysis of the dynamics of a delayed HIV pathogenesis model

AbstractIn this paper, considering full Logistic proliferation of CD4+ T cells, we study an HIV pathogenesis model with antiretroviral therapy and HIV replication time. We first analyze the existence and stability of the equilibrium, and then investigate the effect of the time delay on the stability of the infected steady state. Sufficient conditions are given to ensure that the infected steady state is asymptotically stable for all delay. Furthermore, we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold, and investigate the existence of Hopf bifurcation by using a delay τ as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the main results

Understanding the role of electrons in the magnetism of a colossal permittivity dielectric material

Creating new materials that show potential for technological devices is one of the most important and active areas of solid state chemistry and physics. For data storage, multiferroics present some great advantages due to the coupling of their electrical and magnetic properties. The discovery of In and Nb co-doped rutile (Hu et al. Nat. Mater. 12, 821) presented a material that was perfect for capacitive devices; with high permittivity and low loss, which was attributed to localised polarisable defects within the crystal structure, though other work has suggested internal blocking barriers at grain boundaries as being responsible for the dielectric properties. Here we report on the magnetic properties of this material and shown that magnetic ordering occurs at room temperature and below, with the Curie temperature depending upon doping levels. Moreover, muon spin relaxation measurements suggest that the magnetic order is confined to grain boundaries or areas where the defects can cluster. This implies that a strong magneto-electronic coupling could exist within In- and Nb-co-doped rutile close to room temperature, though the inhomogeneous nature of the magnetism suggests that the coupling may be optimised in nanoparticles or thin films where defect clustering could be promoted

Negative magnetodielectric effect in CaCu₃Ti₄O₁₂

Real part of complex relative dielectric value is relatively decreased as large as  ∼5 % from 50 K to 200 K in CaCu₃Ti₄O₁₂, by applying a 6-T static magnetic field. CaCu₃Ti₄O₁₂ is thus implied primarily by the negative magnetodielectric effect, as a unified dielectric system in which 1-D finite dipole chains of B-site titanium ions, coexist with a collective of polaron-like 3d-electrons of A-site copper ions: the dipole chains are thermally activated for lattice ionic polarization above 50 K, and suppressed by the short-range hop of these quasi-particles, while their long-range movement are for bulk electronic polarization above 151 K.This work was supported by the National Natural Science Foundation of China (Grant No. 11004106) and the National 973 Project (Nos. 2011CB922101 and 2009CB623303)