# D'Onofrio chemotherapy model

D'Onofrio chemotherapy model | |
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State dimension: | 1 |

Differential states: | 4 |

Continuous control functions: | 2 |

Path constraints: | 4 |

This cancer chemotherapy model is based on the work of d'Onofrio. The corresponding dynamic describes the effect of two different drugs administered to the patient. An anti-angiogetic drug is used to suppress the formation of blood vessels from existing vessels and thereby starving the tumors supply of proliferating vessels. In addition a cytostatic drug effects the proliferation of the tumor cells directly. The dynamic of the problem is given by an ODE model.

## Contents

## Mathematical formulation

For the optimal control problem is given by

where the control denotes the administered amount of anti-angiogetic drugs and the amount of cytostatic drugs. The state describes the volume of tumor and the volume of neighboring blood vessels. The remaining states and are used to constraint the maximum amount of drugs over the duration of the therapy.

## Parameters

In the model these parameters are fixed.

The parameters can be taken from the parameter sets shown in the following section. To the remaining parameters exists no experimental data.

## Reference Solutions

The problem can be solved with the [multiple shooting method]. For the following solutions the control functions and states are discretized on the same grid, with 100 nodes. The unknown parameters are chosen from the following parameter sets

Parameter set 1

Parameter set 2

Parameter set 3

Parameter set 4

Furthermore in the objective function is chosen.

## Variants

- a variant where partial outer convexification is applied on the control and the continous control is replaces by binary controls, see also D'Onofrio model (binary variant),

## Source Code

## References

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