The research activities of this group go in two directions. The first one is focused on the analysis of the dynamics and control of systems appearing in modeling of novel therapies for cancer, Newest methods of geometric optimal control are applied with the goal of constructing the so-called regular synthesis of optimal solutions in the sense of Boltyansky. These solutions are expected to provide benchmarks for constructing realizable treatment protocols.The second direction concerns the formulation of mathematical models describing the dynamics of the transmission of a parasite in the population of mosquitos and humans in the presence of drugs blocking transmission of the parasite or interrupting its life cycle. This analysis can be used in preparing and applying treatments in a way that they are the most effective in the control of malaria leading to its complete elimination.

Team Members: Jacek Banasiak, Urszula Ledzewicz, Heinz Schaettler (Washington University, USA)

Relevant Publications:
H. Schaettler, U. Ledzewicz, Optimal Control for Mathematical Models of Cancer Therapies - An Application of Geometric Methods, Springer – Verlag, Interdisciplinary Applied Mathematics, Vol. 42, October 2015, 496 pages.
U. Ledzewicz, H. Schaettler, On the Role of Pharmacometrics in Mathematical Models for Cancer Treatments, Discrete and Continuous Dynamical Systems, series B, Vol. 26(1), 2021, pp. 483-499, DOI: 10.3934/dcdsb.2020213.
Ngwa G.A., Banasiak J. et al, On a three-stage structured model for the dynamics of malaria transmission with human treatment, adult vector demographics and one aquatic stage, Journal of Theoretical Biology, v. 481, pp. 202 – 22221, 2019.
Woldegerima W.A., Ouifki R., Banasiak J., Mathematical analysis of the impact of transmission-blocking drugs on the population dynamics of malaria, Applied Mathematics and Computation, v. 4001, 2021, Article 126005.

All Research Groups