Abstract

The main goal of this paper is to establish the first order necessary optimality conditions for a tumor growth model that evolves due to cancer cell proliferation. The phenomenon is modeled by a system of three-dimensional partial differential equations. We prove the existence and uniqueness of optimal control and necessary conditions of optimality are established by using the variational formulation.

Highlights

  • Mathematical models are increasingly used, in medicine

  • In a continuous model, elements are described in terms of population density and their actions are modelled by partial differential equations: this is an advantage for studying the mathematical properties of the model, but it makes it difficult to establish direct links between model parameters and physical measurements

  • The interpretation of biological phenomena as a result of a set of optimal control problems has not yet been considered by current biomathematics. In this respect, using non-linear dynamic models as a starting point, the aim of this paper is to show how this application of optimal control theory is a promising approach for the analysis of biomedical questions, i.e. to establish the necessary optimality conditions on a dynamic system on which one can act by means of a command to go from a given initial state to a very precise final state

Read more

Summary

Introduction

Mathematical models are increasingly used, in medicine. Formalising biological phenomena such as tumours (Robiyn, 2004), which is the subject of our research, is a hot topic both elsewhere and in Cote d’Ivoire. In addition to these well-known applications, optimal control theory is the most appropriate approach for studying biological phenomena understood as the result of the behaviour of semi-autonomous bio-entities. The interpretation of biological phenomena as a result of a set of optimal control problems has not yet been considered by current biomathematics In this respect, using non-linear dynamic models as a starting point, the aim of this paper is to show how this application of optimal control theory is a promising approach for the analysis of biomedical questions, i.e. to establish the necessary optimality conditions on a dynamic system on which one can act by means of a command to go from a given initial state to a very precise final state.

Mathematical Models for Tumour Dynamics
Notations and Functional Framework
The Formulation of the Optimal Control Problem
Adjoint System
Variation Calculation
Necessary and Sufficient Condition of Optimality
Conclusion
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call