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Ádám Besenyei

Publications and source records attributed to Ádám Besenyei.

3 recordsLinked to original sources
arXiv2015

Bounds for the expected value of one-step processes

Mean-field models are often used to approximate Markov processes with large state-spaces. One-step processes, also known as birth-death processes, are an important class of such processes and are processes with state space $\{0,1,\ldots,N\}$ and where each transition is of size one. We derive explicit bounds on the expected value of such a process, bracketing it between the mean-field model and another simple ODE. Our bounds require that the Markov transition rates are density dependent polynomials that satisfy a sign condition. We illustrate the tightness of our bounds on the SIS epidemic process and the voter model.

math.DS↗
arXiv2014

Dynamic control of modern, network-based epidemic models

In this paper we make the first steps to bridge the gap between classic control theory and modern, network-based epidemic models. In particular, we apply nonlinear model predictive control (NMPC) to a pairwise ODE model which we use to model a susceptible-infectious-susceptible (SIS) epidemic on non-trivial contact structures. While classic control of epidemics concentrates on aspects such as vaccination, quarantine and fast diagnosis, our novel setup allows us to deliver control by altering the contact network within the population. Moreover, the ideal outcome of control is to eradicate the disease while keeping the network well connected. The paper gives a thorough and detailed numerical investigation of the impact and interaction of system and control parameters on the controllability of the system. The analysis reveals, that for certain set parameters it is possible to identify critical control bounds above which the system is controllable. We foresee, that our approach can be extended to even more realistic or simulation-based models with the aim to apply these to real-world situations.

math.CA↗