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A mathematical model of chemotherapy with variable infusion

  • *Corresponding author

    *Corresponding author

Dedicated to Prof. Dr. Tomás Caraballo's 60th birthday

This work was partially supported by Simons Foundation, USA (Collaboration Grants for Mathematicians No. 429717)

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  • A nonautonomous mathematical model of chemotherapy cancer treatment with time-dependent infusion concentration of the chemotherapy agent is developed and studied. In particular, a mutual inhibition type model is adopted to describe the interactions between the chemotherapy agent and cells, in which the chemotherapy agent is modeled as the prey being consumed by both cancer and normal cells, thereby reducing the population of both. Properties of solutions and detailed dynamics of the nonautonomous system are investigated, and conditions under which the treatment is successful or unsuccessful are established. It can be shown both theoretically and numerically that with the same amount of chemotherapy agent infused during the same period of time, a treatment with variable infusion may over perform a treatment with constant infusion.

    Mathematics Subject Classification: Primary: 34D45, 35B41, 37B55; Secondary: 92C50, 97M60.


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  • Figure 1.  Chemotherapy with time-dependent infusion $ \mu(t) = 4 + 2 \sin 0.04 t $, resulting a successful treatment where all cancer cells are removed and normal cells remain

    Figure 2.  Chemotherapy with time-dependent infusion $ \hat{\mu} = 4 $, resulting a failed treatment where all normal cells are removed and cancer cells remain

    Table 1.  Description of parameters in the chemotherapy model

    Parameter Description
    $ b_{1} $ (1/time) Per capita growth rate of cancer cells
    $ b_{2} $ (1/time) Per capita growth rate of normal cells
    $ \kappa_{1} $ (mass/vol) Environmental carrying capacity of cancer cells
    $ \kappa_{2} $ (mass/vol) Environmental carrying capacity of normal cells
    $ d_1 $ (vol/time$ \cdot $mass) Intraspecific competition coefficient of cancer on normal cells
    $ d_2 $ (vol/time$ \cdot $mass) Intraspecific competition coefficient of normal on cancer cells
    $ r_1 $ (1) Consumption effectiveness of cancer cells on the agent
    $ r_2 $ (1) Consumption effectiveness of normal cells on the agent
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