Force-induced deformations of a self-avoiding chain confined inside a cylindrical cavity, with diameter D, are probed using molecular dynamics simulations, scaling analysis, and analytical calculations. We obtain and confirm a simple scaling relation -fD approximately R(-9/4) in the strong-compression regime, while for weak deformations, we find fD = -A(R/R0) + B(R/R0)(-2), where A and B are co...

We study a model of disease transmission with continuous age-structure for latently infected individuals and for infectious individuals. The model is very appropriate for tuberculosis. Key theorems, including asymptotic smoothness and uniform persistence, are proven by reformulating the system as a system of Volterra integral equations. The basic reproduction number R0 is calculated. For R0 < 1...

A class of virus dynamics model with intracellular delay and nonlinear infection rate of Beddington-DeAngelis functional response is analysed in this paper. By constructing suitable Lyapunov functionals and using LaSalle type theorem for delay differential equations, we show that the global stability of the infection-free equilibrium and the infected equilibrium depends on the basic reproductiv...

Because the latent period and the infectious period of tuberculosis TB are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression SP model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reprod...

We propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages. The models can describe disease progression through multiple latent or infectious stages as in the case of HIV and tuberculosis. Amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment. The m...

Supported by: CIM-Centro Internacional de Matemática CMUC-Centro de Matemática da Universidade de Coimbra UIMAUnidade de Investigação Matemática e Aplicações da Universidade de Aveiro 9:45-10:15 Richard Delanghe, University of Ghent Subclasses of monogenic functions Let Ω ⊂ R be open and let R0,m+1 be the real Cli ord algebra generated by the orthonormal basis e = (e0, e1, ..., em) of the quadr...

The dynamics of an in-host model with general form of target-cell dynamics, nonlinear incidence, and distributed delay are investigated. The model can describe the in vivo infection dynamics of many viruses such as HIV-I, HCV, and HBV. We derive the basic reproduction number R0 for the viral infection and establish that the global dynamics are completely determined by the values of R0: if R0 ≤ ...

In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the ...

We introduce a new class of systems holding Parity Time (PT)-symmetry locally whereas being globally Psymmetric. The potential is globally symmetric, U=U(|r|), and fulfills PT-symmetry with respect to periodically distributed points r0: U(|r0+r|)=U*(|r0-r|) being r0∫ 0. We show that such systems hold novel properties arising from the merging of the two different symmetries, leading to a strong ...

We consider the expected residual minimization formulation of the stochastic R0 matrix linear complementarity problem. We show that the involved matrix being a stochastic R0 matrix is a necessary and sufficient condition for the solution set of the expected residual minimization problem to be nonempty and bounded. Moreover, local and global error bounds are given for the stochastic R0 matrix li...