Gompertz models with periodical treatment and applications to prostate cancer

Leonardo Schultz; Antonio Gondim; Shigui Ruan; Leonardo Schultz; Antonio Gondim; Shigui Ruan

doi:10.3934/mbe.2024181

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 3: 4104-4116. doi: 10.3934/mbe.2024181

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Gompertz models with periodical treatment and applications to prostate cancer

Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL 33146, USA
^† These authors contributed equally to this work.

Received: 31 October 2023 Revised: 05 February 2024 Accepted: 13 February 2024 Published: 23 February 2024

In this paper, Gompertz type models are proposed to understand the temporal tumor volume behavior of prostate cancer when a periodical treatment is provided. Existence, uniqueness, and stability of periodic solutions are established. The models are used to fit the data and to forecast the tumor growth behavior based on prostate cancer treatments using capsaicin and docetaxel anticancer drugs. Numerical simulations show that the combination of capsaicin and docetaxel is the most efficient treatment of prostate cancer.
- gompertz model,
- prostate cancer,
- periodic treatment,
- capsaicin,
- docetaxel
Citation: Leonardo Schultz, Antonio Gondim, Shigui Ruan. Gompertz models with periodical treatment and applications to prostate cancer[J]. Mathematical Biosciences and Engineering, 2024, 21(3): 4104-4116. doi: 10.3934/mbe.2024181

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Abstract

In this paper, Gompertz type models are proposed to understand the temporal tumor volume behavior of prostate cancer when a periodical treatment is provided. Existence, uniqueness, and stability of periodic solutions are established. The models are used to fit the data and to forecast the tumor growth behavior based on prostate cancer treatments using capsaicin and docetaxel anticancer drugs. Numerical simulations show that the combination of capsaicin and docetaxel is the most efficient treatment of prostate cancer.

References

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