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\begin{document}

\title{Modeling of drug resistance: comparison of two hypotheses on the example
of LGGs}



\author[1]{Marek Bodnar}%
\author[1]{Urszula Forys}%
\affil[1]{University of Warsaw}%


\vspace{-1em}



  
  \date{May 04, 2024}


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\begin{abstract}
Acquired drug resistance syndrom (ADR) is one of the most important
features associated with tumor treatment and it is therefore
a\textasciitilde{}topic of intensive studies. We present two simple
mathematical models reflecting different mechanisms of ADR with some
Darwinian effects included. These effects allow resistant cells to
become sensitive again. Basing on this mathematical approach we conclude
that for constant continuous treatment, if no Darwinian effects are
present then once resistant cells appear, sensitive cells are eliminated
after a long time, independently of the mechanism of acquiring the
resistance. However, with Darwinian effects the situation is a little
better as the sensitive cells are not completely eliminated but they are
still outcompeted by the resistant ones. Moreover, if the therapy is
stopped resistant cells become dominated by sensitive cells and the
situation changes completely in comparison to the case without Darwinian
effects. We discuss these mechanisms on the example of gliomas.%
\end{abstract}%



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