Session Time & Room : 4E (Aug.24, 17:40-19:20) @G402
Type : Proposal of Minisymposium
Abstract : The mathematical modelling of many biological systems require the application of delay differential equations, since the future evolution of such systems depend of the duration of various processes. Examples range from cell cycle length in cell biology, maturation delay in population dynamics, and latency period in epidemiology . Time delays naturally occur in the control of biological systems as well. On the other hand, delay differential equations pose great challenges from the modelling, analysis, and numerical points of view, especially if nonlinearities are present and the delay is defined in a more involved way, such as state dependent delays. The goal of this minisymposium is to highlight recent advances and novel applications of delay equations in the field of mathematical biology.
Abstract : An approach to modelling bird migration is proposed, in which there is a region
where birds do not move but spend time breeding. Birds leave this breeding region and enter
a migration flyway. Mathematically, the flyway is a curve parametrised by arc-length. Per-capita mortality along the flyway is both position and age-dependent.
[05022] Infectious disease dynamics with delayed control on the reproduction number
Format : Talk at Waseda University
Author(s) :
Ferenc A Bartha (Bolyai Institute, University of Szeged)
Abstract : We attempt to mitigate an epidemic governed by a compartmental transmission model by introducing an adaptive control based on the effective reproduction number $\mathcal{R}_t$. The control aims to keep $\mathcal{R}_t$ within the prescribed interval $\mathcal{I}$ containing 1 by triggering or lifting non-pharmaceutical interventions affecting the transmission rate. The inherent delay in measuring the control output, i.e. $\mathcal{R}_t$, results in involved dynamics. We analyze the effects of both the choice of $\mathcal{I}$ and of the delay.
[04371] A delayed epidemic model for behavior change
Format : Talk at Waseda University
Author(s) :
Toshikazu Kuniya (Kobe University)
Abstract : In the period of COVID-19, the on/off of strict interventions such as lockdown caused oscillations of reported infected population in many countries. In this study, we formulate a delayed epidemic model with psychological effect that people change their contact frequency according to the recent information on the reported cases. We perform the Hopf bifurcation analysis, and show that time delay and behavior change play an important role in the occurrence of the recurrent epidemic waves.
[04511] Evolution of maturation delay
Format : Talk at Waseda University
Author(s) :
Gergely Röst (University of Szeged, Hungary)
Abstract : We propose a new mathematical model to address the evolution of maturation period, building on the well-studied Nicholson's blowfly equation, formulated as a system of delay differential equations with two delays. We identify the optimal maturation delay, depending on the quality and suitability of the habitat, which is both a globally evolutionary stable and convergence stable strategy. Mathematically interesting questions raised by the invasibility of oscillatory insect populations. Joint work with Xingfu Zou.
