Mathematical description of various biological sources and analysis of mathematical models (ordinary differential equations, partial differential equations, delayed equations, differential-integral equations, Markov processes, differential equations) appearing in biomathematics. Mathematical description of cancer and its therapy.

- Delay differential equations, large systems of interacting particles and applications of mathematics in biology and medicine, in particular mathematical models of tumour growth and models of immune system
- Dynamical systems defined by ODE's' and PDE's describing between different population dynamics; modelling of immune reactions and tumour growth dynamics; influence of time delays or/and diffusion on systems stability; biffurcation theory
- Integro-differential equation in biology, nonlocal equations, links between microscopic and macroscopic scales of description: from stochastic semigroups to PDEs, topological chaos and applications in biology
- Evolutionary game theory, population dynamics, statistical mechanics of quasicrystals, stochastic models in biology
- Differential equations with discrete and distributed time delay(s); Cellular automata approach; Mathematical modelling in biology, chemistry and medicine including investigation of: tumour growth, angiogenesis (blood vessels formation process), multicellular spheroids growth and necrotic core formation, cell cycle, tumour-immune system interactions, spreads of the infections, transmissions of multidrug-resistant bacteriae, investigation and optimization of (combined) anticancer therapies and infection control strategies; Mathematical description of the emotional states of communicating people and relationships
- Evolutionary game theory, transfer utility coalitional games, multiperson social dilemmas, population dynamics, learning models, multiagent systems
- Games with a continuum number of players in ecosystems and simplified economies, existence and properties of Nash equilibria in such games, mathematical economy
- Nonlinear partial differential equations; long time behaviour of solutions to evolutionary partial differential equationsl mathematical modelling in biology: prey-predator interactions in aquatic ecosystems; interactions between biological cells with external molecular agents: chemotaxis, receptor mediated morphogen transport in a tissue