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Eradication-resolution dynamics with stochastic flare-ups

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Berg, Hugo van den, 1968- and Duncombe, Zoe A.. (2010) Eradication-resolution dynamics with stochastic flare-ups. Journal of Theoretical Biology, Vol.264 (No.3). pp. 962-970. ISSN 0022-5193

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Official URL: http://dx.doi.org/10.1016/j.jtbi.2010.03.010

Abstract

In infectious disease as well as in cancer, the ultimate outcome of the curative response, mediated by the body itself or through drug treatment, is either successful eradication or a resurgence of the disease (“flare-up” or “relapse”), depending on random fluctuations that dominate the dynamics of the system when the number of diseased cells has become very low. The presence of a low-numbers bottle-neck in the dynamics, which is unavoidable if eradication is to take place at all, renders at least one phase of the dynamics essentially stochastic. However, the eradicating agents (e.g. immune cells, drug molecules) generally remain at high numbers during the critical bottle-neck phase, sufficiently so to warrant a deterministic treatment. This leads us to consider a hybrid stochastic-deterministic approach where the infected cells are treated stochastically whereas the eradicating agents are treated deterministically. Exploiting the fact that the number of eradicating agents typically decreases monotonically during the resolution phase of the response, we derive a set of coupled first-order differential equations that describe the probability of ultimate eradication as a function of the system's state, and we consider a number of biomedical applications.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics R Medicine > RC Internal medicine
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Infection -- Mathematical models, Cancer -- Mathematical models, Stochastic processes
Journal or Publication Title:	Journal of Theoretical Biology
Publisher:	Elsevier
ISSN:	0022-5193
Date:	7 June 2010
Volume:	Vol.264
Number:	No.3
Number of Pages:	9
Page Range:	pp. 962-970
Identification Number:	10.1016/j.jtbi.2010.03.010
Status:	Peer Reviewed
Access rights to Published version:	Open Access
References:	Alfonsi, A., Canc`es, E., Turinici, G., Di Ventura, B., Huisinga, W., 2005. Adaptive simulation of hybrid stochastic and deterministc models for biochemical systems. ESAIM: Proceedings, 1–10. Araujo, R. P., McElwain, D. L., 2004. A history of the study of solid tumour growth: The contribution of mathematical modelling. Bull. Math. Biol. 66 (5), 1039–1091. Badovinac, V. P., Harty, J. T., 2006. Programming, demarcating, and manipulating CD8+ T-cell memory. Immunological Reviews 211, 67–80. Badovinac, V. P., Porter, B. B., Harty, J. T., 2002. Programmed contraction of CD8+ T cells after infection. Nature Immunol. 3, 619 – 626. Bargou, R., Leo, E., Zugmaier, G., Klinger, M., Goebeler, M., Knop, S., Noppeney, R., Viardot, A., Hess, G., Schuler, M., Einsele, H., Brandl, C., Wolf, A., Kirchinger, P., Klappers, P., Schmidt, M., Riethm¨uller, G., Reinhardt, C., Baeuerle, P. A., Kufer, P., 2008. Tumor regression in cancer patients by very low doses of a T cell–engaging antibody. Science 321, 974–977. Berg, H. A. van den., Kiselev, Y. N., 2004. Expansion and contraction of the cytotoxic T lymphocyte response—an optimal control approach. Bull. Math. Biol. 66, 1345 – 1369. Burden, R. L., Faires, J. D., 1989. Numerical Analysis, 4th Edition. PWS-Kent Publishing Company, Boston. de Pillis, L. G., Radunskaya, A. E.,Wiseman, C. L., 2005. A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Research 65, 7950–7958. Harty, J. T., Badovinac, V. P., 2008. Shaping and reshaping CD+ T-cell memory. Nature Rev. Immunol. 8, 107–119. Hirsch, M. W., Smale, S., Devaney, R. L., 2004. Differential Equations, Dynamical Systems, and an Introduction to Chaos. Elsevier. Hudis, C. A., 2007. Trastuzumab — Mechanism of action and use in clinical practice. New Engl. J. Med. 357, 39–51. Karlin, S., Taylor, H. M., 1975. A First Course in Stochastic Processes, 2nd Edition. Academic Press. Kiehl, T. R., Mattheyses, R. M., Simmons, M. K., 2004. Hybrid simulation of cellular behavior. Bioinformatics 20, 316–322. Kottilil, S., Bowmer, M. I., Trahey, J., Howley, C., Gamberga, J., Granta, M. D., 2001. Fas/FasL-independent activation-induced cell death of T lymphocytes from HIV-infected individuals occurs without DNA fragmentation. Cell. Immunol. 214, 1–11. L¨offler, A., Kufer, P., Lutterb¨use, R., Zettl, F., Daniel, P. T., Schwenkenbecher, J. M., Riethm¨uller, G., D¨orken, B., Bargou, R. C., 2000. A recombinant bispecific single-chain antibody, CD19 CD3, induces rapid and high lymphoma-directed cytotoxicity by unstimulated T lymphocytes. Blood 95, 2098–2103. Melero, I., Hervas-Stubbs, S., Glennie, M., Pardoll, D. M., Chen, L., 2007. Immunostimulatory monoclonal antibodies for cancer therapy. Nature Rev. Cancer 7, 95–106. Sachs, R. K., Hlatky, L., 2010. A rapid-mutation approximation for cell population dynamics. Bull. Math. Biol. 72 (2), 359–374. Strasser, A., Pellegrini, M., 2004. T-lymphocyte death during shutdown of an immune response. TRENDS Immunol. 25, 610–615. Wilkinson, D. J., 2006. Stochastic Modelling for Systems Biology. Chapman and Hall. Xu, X.-N., Purbhoo, M. A., Chen, N., Mongkolsapaya, J., Cox, J. H., Meier, U.-C., Tafuro, S., Dunbar, P. R., Sewell, A. K., Hourigan, C. S., Appay, V., Cerundolo, V., Burrows, S. R., McMichael, A. J., Screaton, G. R., 2001. A novel approach to antigen-specific deletion of CTL with minimal cellular activation using a3 domain mutants of MHC class I/peptide complex. Immunity 14, 591–602.
URI:	http://wrap.warwick.ac.uk/id/eprint/3856