Mathematical modeling of glioma therapy using oncolytic viruses

Baba Issa Camara; Houda Mokrani; Evans K. Afenya

doi:10.3934/mbe.2013.10.565

Article Contents

2013, Volume 10, Issue 3: 565-578. Doi: 10.3934/mbe.2013.10.565

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Mathematical modeling of glioma therapy using oncolytic viruses

1.
Laboratoire Interdisciplinaire des Environnements Continentaux, Université de Lorraine, CNRS UMR 7360, 8 rue du Général Delestraint, 57070 METZ
2.
Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, UMR 6085 CNRS, Avenue de l'Université, 76801 Saint Etienne du Rouvray
3.
Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126

Received: June 2012

Revised: February 2013

Published: March 2013

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Abstract

Diffuse infiltrative gliomas are adjudged to be the most common primary brain tumors in adults and they tend to blend in extensively in the brain micro-environment. This makes it difficult for medical practitioners to successfully plan effective treatments. In attempts to prolong the lengths of survival times for patients with malignant brain tumors, novel therapeutic alternatives such as gene therapy with oncolytic viruses are currently being explored. Based on such approaches and existing work, a spatio-temporal model that describes interaction between tumor cells and oncolytic viruses is developed. Conditions that lead to optimal therapy in minimizing cancer cell proliferation and otherwise are analytically demonstrated. Numerical simulations are conducted with the aim of showing the impact of virotherapy on proliferation or invasion of cancer cells and of estimating survival times.

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Mathematics Subject Classification: Primary: 92C37, 35B35; Secondary: 35B40.

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