Anti-It\^o noise-induced phase transitions in tumor growth with chemotherapy

TL;DR

This paper models tumor growth under chemotherapy using Hänggi-Klimontovich stochastic differential equations, demonstrating that this approach yields more biologically realistic phase transition results compared to Itô-based models.

Contribution

It introduces the use of Hänggi-Klimontovich stochastic integrals in tumor growth modeling, highlighting their advantages over Itô integrals for biological systems.

Findings

Hänggi-Klimontovich SDEs produce more realistic tumor growth phase transitions.

Comparison shows differences between Itô and Hänggi-Klimontovich models.

Hänggi-Klimontovich approach better captures biological variability.

Abstract

The objective of this work is to apply the H\"anggi-Klimontovich stochastic differential equations to model and study the effects of anti-tumor chemotherapy in the case of continuous infusion delivering. The fluctuations generated by variations in drug concentration are modeled by the H\"anggi-Klimontovich stochastic integral. This integral, which in the physics literature is sometimes called anti-It\^o integral, in the last decade it has been referenced quite as the more appropriate stochastic integral for model various biological and physical systems. Then, we make some comparisons with the model based on It\^o stochastic differential equations and their phase transitions that they generate, showing that the H\"anggi-Klimontovich stochastic differential equations lead to more biologically realistic results.