Background: Various mathematical models have been proposed for studying the growth
of tumor cells under chemotherapeutic drug administration. In most of the deterministic models, the
drug is administered as per the rate equation of time.
Objective: In this paper we have studied the behavior of a predator-prey model when the drug infusion
rate is governed by a sinusoidal function.
Method: A logistic growth model, to study the response of tumor growth to chemotherapeutic drug
dosage is considered. The model has been suitably modified to introduce periodic drug infusion rate
which is a sinusoidal function. In this paper, an extensive sensitivity analysis on the parameters, tumor
cells division rate, cell kill rate, rate at which the drug becomes ineffective and the drug decay
rate has been carried out to determine how these parameters affect the growth of the tumor and how
the drug accumulates in the body.
Results: 1000 sets of these four parameters were randomly chosen from appropriate Gamma distributions
and corresponding curves for the number of tumor cells and average drug accumulation
have been obtained. A comparative study of drug administration at a constant rate and at a periodic
rate has been done. Effect of changes in the parameters governing the drug infusion rate have been
analyzed and how the parameters used in the model relate to pharmacokinetics and pharmacodynamics
of a drug has been pointed out.
Conclusion: We have been able to show that controlled periodic drug infusion is a better strategy
than administering the drug of a constant rate.