zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Analysis of wave solutions of an adhenovirus-tumor cell system. (English) Zbl 1237.35156
Summary: We discuss the biological background and the mathematical analysis of glioma gene therapy for contributing to cancer treatment. By a reaction-diffusion system, we model interactions between gliom cells and viruses. We establish some sufficient conditions on model parameters which guarantee the permanence of the system and the existence of periodic solutions. Our study has experimental and theoretical implications in the prospective management strategy of therapy.

MSC:
35Q92PDEs in connection with biology and other natural sciences
92C50Medical applications of mathematical biology
35K57Reaction-diffusion equations
35B10Periodic solutions of PDE
WorldCat.org
Full Text: DOI
References:
[1] A. Claes, A. J. Idema, and P. Wesseling, “Diffuse glioma growth: a guerilla war,” Acta Neuropathologica, vol. 114, no. 5, pp. 443-458, 2007. · doi:10.1007/s00401-007-0293-7
[2] J. R. Bischoff, D. H. Kirn, A. Williams et al., “An adenovirus mutant that replicates selectively in p53-deficient human tumor cells,” Science, vol. 274, no. 5286, pp. 373-376, 1996. · doi:10.1126/science.274.5286.373
[3] C. Heise, A. Sampson-Johannes, A. Williams, F. McCormick, D. D. Von Hoff, and D. H. Kirn, “ONYX-015, an E1b gene-attenuated adenovirus, causes tumor-specific cytolysis and antitumoral efficacy that can be augmented by standard chemotherapeutic agents,” Nature Medicine, vol. 3, no. 6, pp. 639-645, 1997. · doi:10.1038/nm0697-639
[4] E. A. Chiocca, K. M. Abbed, S. Tatter et al., “A phase I open-label, dose-escalation, multi-institutional trial of injection with an E1B-attenuated adenovirus, ONYX-015, into the peritumoral region of recurrent malignant gliomas, in the adjuvant setting,” Molecular Therapy, vol. 10, no. 5, pp. 958-966, 2004. · doi:10.1016/j.ymthe.2004.07.021
[5] N. L. Komarova, “Mathematical modeling of tumorigenesis: mission possible,” Current Opinion in Oncology, vol. 17, no. 1, pp. 39-43, 2005. · doi:10.1097/01.cco.0000143681.37692.32
[6] A. S. Novozhilov, F. S. Berezovskaya, E. V. Koonin, and G. P. Karev, “Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the framework of deterministic models,” Biology Direct, vol. 1, article no. 6, 2006. · doi:10.1186/1745-6150-1-6
[7] J. T. Oden, A. Hawkins, and S. Prudhomme, “General diffuse-interface theories and an approach to predictive tumor growth modeling,” Mathematical Models & Methods in Applied Sciences, vol. 20, no. 3, pp. 477-517, 2010. · Zbl 1186.92024 · doi:10.1142/S0218202510004313
[8] D. Wodarz, “Viruses as antitumor weapons: defining conditions for tumor remission,” Cancer Research, vol. 61, no. 8, pp. 3501-3507, 2001.
[9] D. Wodarz and N. Komarova, Computational Biology of Cancer: Lecture Notes And Mathematical Modelin, World Scientific, Singapour, 2005. · Zbl 1126.92029
[10] B. I. Camara, H. Mokrani, and E. Afenya, “Mathematical modelling of gliomas therapy using oncolytic viruses,” to appear. · Zbl 1268.92058
[11] W. Walter, “Differential inequalities and maximum principles: theory, new methods and applications,” vol. 30, no. 8, pp. 4695-4711, 1997. · Zbl 0893.35014 · doi:10.1016/S0362-546X(96)00259-3
[12] H. L. Smith, “Dynamics of competition,” in Mathematics Inspired by Biology, vol. 1714 of Lecture Notes in Math., pp. 191-240, Springer, Berlin, Germany, 1999. · Zbl 1002.92564