Juraj Földes

A mathematical model for cell cycle-specific cancer virotherapy.

Oncolytic viruses preferentially infect and replicate in cancerous cells, leading to elimination of tumour populations, while sparing most healthy cells. Here, we study the cell cycle-specific activity of viruses such as vesicular stomatitis virus (VSV). In spite of its capacity as a robust cytolytic agent, VSV cannot effectively attack certain tumour cell types during the quiescent, or resting, phase of the cell cycle. In an effort to understand the interplay between the time course of the cell cycle and the specificity of VSV, we develop a mathematical model for cycle-specific virus therapeutics. We incorporate the minimum biologically required time spent in the non-quiescent cell cycle phases using systems of differential equations with incorporated time delays. Through analysis and simulation of the model, we describe how varying the minimum cycling time and the parameters that govern viral dynamics affect the stability of the cancer-free equilibrium, which represents therapeutic success.

Asymptotic Analysis for Randomly Forced MHD

We consider the three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the Earths fluid core. We examine the multi-parameter singular limit of vanishing Rossby number

On the Born–Infeld equation for electrostatic fields with a superposition of point charges

\epsilon

Equilibria with a nontrivial nodal set and the dynamics of parabolic equations on symmetric domains

and magnetic Reynolds number

On asymptotically symmetric parabolic equations

\delta

On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry

, and establish that: (i) the limiting stochastically driven active scalar equation (with

Ergodic and mixing properties of the Boussinesq equations with a degenerate random forcing

\epsilon =\delta=0

Convergence to a steady state for asymptotically autonomous semilinear heat equations on RN

) possesses a unique ergodic invariant measure, and (ii) any suitable sequence of statistically invariant states of the full MHD system converge weakly, as

On symmetry properties of parabolic equations in bounded domains

\epsilon,\delta \rightarrow 0

Symmetry of Positive Solutions of Asymptotically Symmetric Parabolic Problems on

, to the unique invariant measure of the limit equation. This latter convergence result does not require any conditions on the relative rates at which