A caution for oncologists: chemotherapy can cause chaotic dynamics

The effect of chemotherapy in cancer models is mostly handled by using a separate equation for chemotherapeutic agent. In this study, we do not consider a separate equation for drug but rather introduce its effect in terms of a parameter m representing the fraction of tumor cells killed by chemotherapeutic drug module. The main objective of this study is to provide conditions on model parameters which when fulfilled the grave consequences of cancer can be avoided. This study also shows that chemotherapy at times can produce unexpected results.

Linearization method to study the stability of model equilibria.

The results obtained in this study are governed by the trichotomy law on the number 1-a₁₂-d₁, where a₁₂ represents the negative effect on the growth of cancer cells due to their competition with host cells for resources and d₁ is rate of annihilation of cancer cells due to chemotherapy. It is seen that in case of under-dose drug module when d₁<1-a₁₂, the complete eradication of cancer is not possible. When d₁=1-a₁₂, the model suggests occurrence of chaotic dynamics. When the drug dose is properly adjusted so that d₁>1-a₁₂, the complete eradication of cancer is guaranteed.

The results of the model of this paper given for the post vascular stages of tumor suggest criteria to select a particular drug module (a single drug or a combination of drugs) that the chemotherapy procedure should adapt to eradicate cancer. This study injects a note of caution for oncologists that chemotherapy as cancer treatment can also cause chaotic dynamics in certain situations. This study also presents a plausible explanation to the question why sometimes a tumor grows in the body and then gets cured without any medical intervention.