Biology subjects

Röst, G.

Publications and source records attributed to Röst, G..

3 recordsLinked to original sources

bioRxiv2025

A mathematical model for cancer dynamics with treatment and saboteur bacteria

We construct a mathematical model of cancer dynamics with chemotherapeutic treatment, in the presence of bacteria that are capable of metabolizing the chemotherapeutic drug, hence sabotaging the treatment. We investigate the possibility of complementing the cancer treatment with antibiotic drugs, thus eradicating the bacteria or at least mitigating their negative impact on the prospects of therapy. Our model is a nonlinear system of four differential equations, for which we perform a complete analysis, explicitly characterizing the four possible outcomes, depending on whether the cancer cells or the bacteria extinct or persist. Global stability results are proven by the iterative application of a comparison principle, and a bifurcation diagram is created to show the transitions between scenarios with respect to the controllable parameters. We apply our model to an experiment on mice with colon cancer and the drug Gemcitabine.

cancer biology↗

bioRxiv2021

Unidirectional migration of populations with Allee effect

In this note we consider two populations living on identical patches, connected by unidirectional migration, and subject to strong Allee effect. We show that by increasing the migration rate, there are more bifurcation sequences than previous works showed. In particular, the number of steady states can change from 9 (small migration) to 3 (large migration) at a single bifurcation point, or via a sequences of bifurcations with the system having 9,7,5,3 or 9,7,9,3 steady states, depending on the Allee threshold. This is in contrast with the case of bidirectional migration, where the number of steady states always goes through the same bifurcation sequence of 9,5,3 steady states as we increase the migration rate, regardless of the value of the Allee threshold.

ecology↗

bioRxiv2021

A hybrid PDE-ABM model for viral dynamics with application to SARS-CoV-2 and influenza

We propose a hybrid partial differential equation - agent-based (PDE-ABM) model to describe the spatio-temporal viral dynamics in a cell population. The virus concentration is considered as a continuous variable and virus movement is modelled by diffusion, while changes in the states of cells (i.e. healthy, infected, dead) are represented by a stochastic agent-based model. The two subsystems are intertwined: the probability of an agent getting infected in the ABM depends on the local viral concentration, and the source term of viral production in the PDE is determined by the cells that are infected. We develop a computational tool that allows us to study the hybrid system and the generated spatial patterns in detail. We systematically compare the outputs with a classical ODE system of viral dynamics, and find that the ODE model is a good approximation only if the diffusion coefficient is large. We demonstrate that the model is able to predict SARS-CoV-2 infection dynamics, and replicate the output of in vitro experiments. Applying the model to influenza as well, we can gain insight into why the outcomes of these two infections are different.

systems biology↗