gabriele-codega/tumor-dynamics

Python implementation of some utilities to study the stochastic dynamics of tumours.

Tumor dynamics

This code implements some utilities to study the stochastic dynamics of the interaction between a tumor and immune system in presence of chemotherapy.

The model is implemented according to what proposed in this paper (which in turn is an extension of the model proposed by Kuznetsov et al.).

TumorDynamics

The files are organised as follows

immune_system.py

Implements a class (DeterministicImmuneSystem) for the representation of the immune system. Its main features are:

• a function that defines the rhs of the dynamical system describing the evolution of the system
• a method to integrate the system and get its evolution in time
• methods to compute the period of limit cycles
• a method to plot the phase space trajectory

stochastic_system.py

Implements a StochasticImmuneSystem, that inherits from DeterministicImmuneSystem and represents an immune system in presence of a disturbance in the intensity of chemotherapy. Its main features are:

• a function that describes the stochastic part of the system
• methods to integrate the equations and simulate random trajectories
• methods to compute the stochastic sensitivity matrix and function
• a method to plot the phase space trajectory

plotting_utils.py

Utilities to build confidence bands and ellipses, using the method of stochastic sensitivity function (see for instance this paper).