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Session 21. Mathematical models for biological invasion
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Prostate cancer: preventing invasion by immunotherapy |
Urszula Foryś, University of Warsaw, Poland
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The talk is based on the joint work with Marek Bodnar
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Our analysis is motivated by the PC immunotherapy model proposed in Kronik et al. [1]. It occurs that asymptotically this model has one dimensional dynamics. Moreover, this dynamics is simple when only one boost is given, as we obtain an autonomous equation with the right-hand side being a monotonic function. Therefore, we easily study the behaviour of solutions. On the other hand, applying the treatment periodically, we asymptotically obtain a \(t\)-periodic right-hand side of the equation.
We present a general result concerning asymptotic dynamics of one ODE with the right hand-side \(f(t,x)\) being \(t\)-periodic and monotonic in \(x\). Next, we apply the general results to the PC immunotherapy model.
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References- N. Kronik, Y. Kogan, M. Elishmereni, K. Halevi-Tobias, S. Vuk-Pavlovic, et al., Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models , PLoS ONE, 5(12), 2010, e15482.
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