01Research interests
Six interlocking themes, one question: what do the equations say about the long-term fate of a biological system?
ẋ = f(x)Differential equations
Differential equations are the mathematical descriptions of physical and biological systems that continuously change in time. These equations are defined by relationships between the current state of the system and the rate of its change. Our goal is to predict the future behaviour of the system, using analytic, qualitative or numerical investigations of the solutions.
R₀ = ϱ(FV⁻¹)Mathematical epidemiology
Mathematical models can predict how infectious diseases progress to show the likely outcome of an epidemic. By disease modelling we can provide important information to public health by designing, evaluating and comparing different strategies to control the outbreak. The basic mathematical framework uses systems of differential equations called compartmental models.
x ↦ λx(1−x)Nonlinear dynamics
Nonlinear dynamics describe the time evolution of systems where the output is not proportional to the input. To understand complex systems we need to take into account all the interactions of variables and complicated feedbacks. A major goal is to describe the geometric structure of attractors, that encapsulate the most important information about the long term dynamics.
ẋ(t) = f(x(t−τ))Time delays
Time delays arise in various fields of engineering, physics and biology. Dynamical systems including delays can be written as delay differential equations (DDEs). Their right hand side is a functional, and the corresponding phase space is infinite dimensional. Nonlinear DDEs can show very interesting dynamics and lead to fascinating and sophisticated mathematics.
∂ₜu = D∇²u + f(u)Modelling of cell biology processes
Cell proliferation, death and motility are key events in many important cell biological processes, such as embryonic development, tissue regeneration or the progression of cancer. Mathematical models help to understand the collective behaviour and the spatio-temporal dynamics of various cell populations, which may lead to, for example, more efficient treatments of cancer.
λ(μ) = 0Bifurcation theory
Bifurcations represent situations when the behaviour of a system suddenly changes as a parameter is crossing a critical value. They are associated to loss of stability, the appearance or destruction of equilibria, sudden emergence of periodic or more complex behaviours. The birth of chaos from simple dynamics can be understood through a cascade of subsequent bifurcations.
02Epidemic sandbox
A classic SIR / SEIR model running live in your browser. Move the sliders: see how transmissibility, vaccination coverage and latency shape the curve. (Illustrative toy model — not a forecast.)
03Research Projects
Grants and collaborations. PI principal investigator · co-PI co-principal investigator · part. participant · sup. supervisor.
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04In the media
Interviews, articles and lectures on epidemic modelling and health security. The full searchable archive has filters by type, language and year, and an in-page video player.
05Gallery
Click a photo to enlarge.
06Contact
Bolyai Institute, University of SzegedAradi vértanúk tere 1, H-6720 Szeged, Hungary
tel.: +36 62 54-4098 · email: info@eglab.hu