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- Gergely Röst, Jianhong Wu
- Mathematical biosciences and engineering : MBE
- 2008

A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if… (More)

- Murray E. Alexander, Christopher S. Bowman, +5 authors Ping Yan
- Proceedings. Biological sciences
- 2007

Given the danger of an unprecedented spread of the highly pathogenic avian influenza strain H5N1 in humans, and great challenges to the development of an effective influenza vaccine, antiviral drugs will probably play a pivotal role in combating a novel pandemic strain. A critical limitation to the use of these drugs is the evolution of highly transmissible… (More)

- Seyed M. Moghadas, Christopher S. Bowman, Gergely Röst, Jianhong Wu
- PloS one
- 2008

BACKGROUND
The emergence of neuraminidase inhibitor resistance has raised concerns about the prudent use of antiviral drugs in response to the next influenza pandemic. While resistant strains may initially emerge with compromised viral fitness, mutations that largely compensate for this impaired fitness can arise. Understanding the extent to which these… (More)

- M V Barbarossa, Gergely Röst
- Journal of mathematical biology
- 2015

When the body gets infected by a pathogen the immune system develops pathogen-specific immunity. Induced immunity decays in time and years after recovery the host might become susceptible again. Exposure to the pathogen in the environment boosts the immune system thus prolonging the time in which a recovered individual is immune. Such an interplay of within… (More)

- Murray E. Alexander, Seyed M. Moghadas, Gergely Röst, Jianhong Wu
- Bulletin of mathematical biology
- 2008

The use of antiviral drugs has been recognized as the primary public health strategy for mitigating the severity of a new influenza pandemic strain. However, the success of this strategy requires the prompt onset of therapy within 48 hours of the appearance of clinical symptoms. This requirement may be captured by a compartmental model that monitors the… (More)

- Gergely Röst, Jianhong Wu
- 2007

dynamics of delay differential equations with unimodal feedback BY GERGELY RÖST* AND JIANHONG WU Analysis and Stochastics Research Group, Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, 6720 Szeged, Aradi vértanúk tere 1, Hungary Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York… (More)

- Don A. Jones, Hal L. Smith, Horst R. Thieme, Gergely Röst
- SIAM Journal of Applied Mathematics
- 2012

A reaction diffusion system with time delay is proposed for virus spread on bacteria immobilized on an agar-coated plate. The delay explicitly accounts for a virus latent period of fixed duration. An interval of possible spreading speeds for virus infection is established, and traveling wave solutions are shown to exist. Linear determinacy of spreading… (More)

- Yukihiko Nakata, Gergely Röst
- Journal of mathematical biology
- 2015

We formulate an epidemic model for the spread of an infectious disease along with population dispersal over an arbitrary number of distinct regions. Structuring the population by the time elapsed since the start of travel, we describe the infectious disease dynamics during transportation as well as in the regions. As a result, we obtain a system of delay… (More)

- Gergely Röst
- 2004

In this paper we study the delay differential equation ẋ(t)= (a(t)x(t)+ f (t, x(t − 1))), where is a real parameter, the functions a(t), f (t, ) are C4-smooth and periodic in the variable t with period 1. Varying the parameter, eigenvalues of the monodromy operator (the derivative of the time-one map at the equilibrium 0) cross the unit circle and… (More)

- Gergely Röst
- 2012

We extend the analysis of the global dynamics for a special class of single commodity market models introduced by Bélair and Mackey. In particular, we determine uniform asymptotic bounds for the fluctuating price, and give sufficient conditions for the global convergence to the positive equilibrium.