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Eradication-resolution dynamics with stochastic flare-ups
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Berg, Hugo van den and Duncombe, Zoe A. (2010) Eradication-resolution dynamics with stochastic flare-ups. Journal of Theoretical Biology, Vol.264 (No.3). pp. 962-970. doi:10.1016/j.jtbi.2010.03.010 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 | ||||
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Subjects: | Q Science > QA Mathematics R Medicine > RC Internal medicine |
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Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | 7 June 2010 | ||||
Dates: |
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Volume: | Vol.264 | ||||
Number: | No.3 | ||||
Number of Pages: | 9 | ||||
Page Range: | pp. 962-970 | ||||
DOI: | 10.1016/j.jtbi.2010.03.010 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
Data sourced from Thomson Reuters' Web of Knowledge
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