An elementary mathematical modeling of drug resistance in cancer

Kangbo Bao; Kangbo Bao

doi:10.3934/mbe.2021018

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 339-353. doi: 10.3934/mbe.2021018

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Research article

An elementary mathematical modeling of drug resistance in cancer

Kangbo Bao ^,

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received: 07 September 2020 Accepted: 10 November 2020 Published: 02 December 2020

Targeted therapy is one of the promising strategies for the treatment of cancer. However, resistance to anticancer drug strongly limits the long-term effectiveness of treatment, which is a major obstacle for successfully treating cancer. In this paper, we analyze a linear system of ordinary differential equations for cancer multi-drug resistance induced mainly by random genetic point mutation. We investigate that the resistance generated before the beginning of the treatment is greater than that developed during-treatment. This result depends on the concentration of the drug, which holds only when the concentration of the drug reaches a lower limit. Moreover, no matter how many drugs are used in the treatment, the amount of resistance (generated at the beginning of the treatment and within a certain period of time after the treatment) always depends on the turnover rate. Using numerical simulations, we also evaluate the response of the mutant cancer cell population as a function of time under different treatment strategies. At appropriate dosages, combination therapy produces significant effects for the treatment with low-turnover rate cancer. For cancer with very high-turnover rate (close to 1), combination therapy can not significantly reduce the amount of resistant mutants compared to monotherapy, so in this case, combination therapy would not have advantage over monotherapy.
- drug resistance,
- cancer,
- mutation,
- ordinary differential equations,
- combination therapy
Citation: Kangbo Bao. An elementary mathematical modeling of drug resistance in cancer[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 339-353. doi: 10.3934/mbe.2021018

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Abstract

Targeted therapy is one of the promising strategies for the treatment of cancer. However, resistance to anticancer drug strongly limits the long-term effectiveness of treatment, which is a major obstacle for successfully treating cancer. In this paper, we analyze a linear system of ordinary differential equations for cancer multi-drug resistance induced mainly by random genetic point mutation. We investigate that the resistance generated before the beginning of the treatment is greater than that developed during-treatment. This result depends on the concentration of the drug, which holds only when the concentration of the drug reaches a lower limit. Moreover, no matter how many drugs are used in the treatment, the amount of resistance (generated at the beginning of the treatment and within a certain period of time after the treatment) always depends on the turnover rate. Using numerical simulations, we also evaluate the response of the mutant cancer cell population as a function of time under different treatment strategies. At appropriate dosages, combination therapy produces significant effects for the treatment with low-turnover rate cancer. For cancer with very high-turnover rate (close to 1), combination therapy can not significantly reduce the amount of resistant mutants compared to monotherapy, so in this case, combination therapy would not have advantage over monotherapy.

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