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DePillis2007 - Seeking Bang Bang Solutions of Mixed ImmunoChemotherapy of Tumors

ABSTRACT: SEEKING BANG-BANG SOLUTIONS OF MIXED IMMUNO-CHEMOTHERAPY OF TUMORS LISETTE G. DE PILLIS, K. RENEE FISTER, WEIQING GU, CRAIG COLLINS, MICHAEL DAUB, DAVID GROSS, JAMES MOORE, BEN PRESKILL* Abstract. It is known that a beneficial cancer treatment approach for a single patient often involves the administration of more than one type of therapy. The question of how best to combine multiple cancer therapies, however, is still open. In this study, we investigate the theoretical interaction of three treatment types (two biological therapies and one chemotherapy) with a growing cancer, and present an analysis of an optimal control strategy for administering all three therapies in combination. In the situations with controls introduced linearly, we find that there are conditions on which the controls exist singularly. Although bang-bang controls (on-off) reflect the drug treatment approach that is often implemented clinically, we have demonstrated, in the context of our mathematical model, that there can exist regions on which this may not be the best strategy for minimizing a tumor burden. We characterize the controls in singular regions by taking time derivatives of the switching functions. We will examine these representations and the conditions necessary for the controls to be minimizing in the singular region. We begin by assuming only one of the controls is singular on a given interval. Then we analyze the conditions on which a pair and then all three controls are singular

SUBMITTER: Mohammad Umer Sharif Shohan  

PROVIDER: MODEL2003060001 | BioModels | 2020-03-06


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Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations.

de Pillis LG   Gu W   Radunskaya AE  

Journal of theoretical biology 20050908 4

We develop and analyze a mathematical model, in the form of a system of ordinary differential equations (ODEs), governing cancer growth on a cell population level with combination immune, vaccine and chemotherapy treatments. We characterize the ODE system dynamics by locating equilibrium points, determining stability properties, performing a bifurcation analysis, and identifying basins of attraction. These system characteristics are useful not only to gain a broad understanding of the specific s  ...[more]

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