An elementary approach to modeling drug resistance in cancer
Resistance to drugs has been an ongoing obstacle to a successfultreatment of many diseases. In this work we consider the problem ofdrug resistance in cancer, focusing on random genetic point mutations.Most previous works on mathematical models of such drug resistancehave been based on stochastic me...
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| Format: | Article |
| Language: | English |
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AIMS Press
2010-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.905 |
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| author | Cristian Tomasetti Doron Levy |
| author_facet | Cristian Tomasetti Doron Levy |
| author_sort | Cristian Tomasetti |
| collection | DOAJ |
| description | Resistance to drugs has been an ongoing obstacle to a successfultreatment of many diseases. In this work we consider the problem ofdrug resistance in cancer, focusing on random genetic point mutations.Most previous works on mathematical models of such drug resistancehave been based on stochastic methods. In contrast,our approach is based on an elementary, compartmental system of ordinarydifferential equations.We use our very simple approach to derive resultson drug resistance that are comparable to those that were previously obtained using much more complex mathematical techniques.The simplicity of our model allows us to obtain analytic results forresistance to any number of drugs.In particular, we show that the amountof resistance generated before the start of the treatment, and present at some given time afterward, always depends onthe turnover rate, no matter how many drugs are simultaneously used inthe treatment. |
| format | Article |
| id | doaj-art-b9943393497347d2a466e1625cddf5a6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b9943393497347d2a466e1625cddf5a62025-01-24T02:00:58ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-09-017490591810.3934/mbe.2010.7.905An elementary approach to modeling drug resistance in cancerCristian Tomasetti0Doron Levy1Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742Resistance to drugs has been an ongoing obstacle to a successfultreatment of many diseases. In this work we consider the problem ofdrug resistance in cancer, focusing on random genetic point mutations.Most previous works on mathematical models of such drug resistancehave been based on stochastic methods. In contrast,our approach is based on an elementary, compartmental system of ordinarydifferential equations.We use our very simple approach to derive resultson drug resistance that are comparable to those that were previously obtained using much more complex mathematical techniques.The simplicity of our model allows us to obtain analytic results forresistance to any number of drugs.In particular, we show that the amountof resistance generated before the start of the treatment, and present at some given time afterward, always depends onthe turnover rate, no matter how many drugs are simultaneously used inthe treatment.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.905ordinary differential equationscancerstochastic methods.drugresistance |
| spellingShingle | Cristian Tomasetti Doron Levy An elementary approach to modeling drug resistance in cancer Mathematical Biosciences and Engineering ordinary differential equations cancer stochastic methods. drugresistance |
| title | An elementary approach to modeling drug resistance in cancer |
| title_full | An elementary approach to modeling drug resistance in cancer |
| title_fullStr | An elementary approach to modeling drug resistance in cancer |
| title_full_unstemmed | An elementary approach to modeling drug resistance in cancer |
| title_short | An elementary approach to modeling drug resistance in cancer |
| title_sort | elementary approach to modeling drug resistance in cancer |
| topic | ordinary differential equations cancer stochastic methods. drugresistance |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.905 |
| work_keys_str_mv | AT cristiantomasetti anelementaryapproachtomodelingdrugresistanceincancer AT doronlevy anelementaryapproachtomodelingdrugresistanceincancer AT cristiantomasetti elementaryapproachtomodelingdrugresistanceincancer AT doronlevy elementaryapproachtomodelingdrugresistanceincancer |