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q-bio.PE2018
fails to predict the outbreak potential in the presence of natural-boosting immunity
Yukihiko Nakata, Ryosuke Omori
Time varying susceptibility of host at individual level due to waning and boosting immunity is known to induce rich long-term behavior of disease transmission dynamics. Meanwhile,…
math.DS2018
Delay-induced blow-up in a planar oscillation model
Alexey Eremin, Emiko Ishiwata, Tetsuya Ishiwata +1
In this paper we study a system of delay differential equations from the viewpoint of a finite time blow-up of the solution. We prove that the system admits a blow-up solution, no…
math.DS2018
A periodic solution of period two of a delay differential equation
Yukihiko Nakata
In this paper we prove that the following delay differential equation \[ \frac{d}{dt}x(t)=rx(t)\left(1-\int_{0}^{1}x(t-s)ds\right), \] has a periodic solution of period two for $r>…