In the original publication, the addresses of the authors Dr. J.A.J. Metz and Dr. S. Nakaoka were incorrectly published. The correct address list for the authors are:
J.A.J. Metz: Institute of Biology and Institute of Mathematics, Leiden University, P.O. Box 9516, 2300RA Leiden, The Netherlands. S. Nakaoka: Graduate School of Medicine, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. E-mail: snakaoka@m.u-tokyo.ac.jp.
While working on their paper (Breda et al. 2015), Philipp Getto and Julia Sánchez Sanz found that formula (4.22) is incomplete (indeed, the solution operator of the homogeneous version of the linearized equation (4.3) should act on the second term at the right hand side of (4.22)). As a consequence (4.23), (4.24), (4.25), (4.31) and (4.32) are incorrect as well. Actually, as it turned out, there were additional inaccuracies. The correct formulas are
$$\begin{aligned} D_3\xi (\tau ;a,\bar{S})\psi= & {} \eta (\tau )+e^{\int _{\bar{\tau }}^\tau \frac{\partial g}{\partial \xi }\left( \bar{\xi }(\sigma ),\bar{S} \right) d\sigma }\left( \frac{g(\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}-1\right) \eta (\bar{\tau }) \end{aligned}$$
(4.22)
$$\begin{aligned} D_3\xi (\tau ;a,\bar{S})\psi= & {} \eta (\tau )+e^{\int _{\bar{\tau }}^\tau \frac{\partial g}{\partial \xi }\left( \bar{\xi }(\sigma ),\bar{S} \right) d\sigma }\left( \frac{g(\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}-1\right) \eta (\bar{\tau })H(\tau -\bar{\tau }) \nonumber \\\end{aligned}$$
(4.23)
$$\begin{aligned} D_2\varXi (a;\bar{S})\psi= & {} \int _{0}^{a}K(a,\alpha )\psi (-a+\alpha )d\alpha \nonumber \\&+\,\left( \frac{g(\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}-1\right) \int _{0}^{\bar{\tau }}K(a,\alpha )\psi (-a+\alpha )d\alpha \cdot H(a-\bar{\tau }). \nonumber \\ \end{aligned}$$
(4.24)
$$\begin{aligned} D_2\mathcal {F}(a,\bar{S})\psi= & {} \int _0^a L(a,\theta )\psi (-a+\theta )d\theta -\frac{\mu (\xi _A+,\bar{S})-\mu (\xi _A-,\bar{S})}{g(\xi _A-,\bar{S})}\bar{\mathcal {F}}(a) \nonumber \\&\times \,\int _0^{\bar{\tau }}K(\bar{\tau },\alpha )\psi (-a+\alpha )d\alpha \cdot H(a-\bar{\tau }) \nonumber \\&-\,\left( \frac{g(\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}-1\right) \bar{\mathcal {F}}(a)\nonumber \\&\times \,\int _0^{\bar{\tau }}\int _{\bar{\tau }}^a\frac{\partial \mu }{\partial \xi }\left( \bar{\xi }(\sigma ),\bar{S}\right) K(\sigma ,\alpha )d\sigma \psi (-a+\alpha )d\alpha H(a-\bar{\tau }). \nonumber \\ \end{aligned}$$
(4.25)
$$\begin{aligned} k_{12}(a)= & {} \bar{b}\int _{\max \{0,\bar{\tau }-a\}}^{\infty }\left\{ \beta (\bar{\xi }(a+\theta ),\bar{S})L(a+\theta ,\theta )\right. \nonumber \\&\left. +\,\frac{\partial \beta }{\partial \xi }(\bar{\xi }(a+\theta ),\bar{S})K(a+\theta ,\theta )\bar{\mathcal {F}}(a+\theta )\right\} d\theta \nonumber \\&+\,\bar{b}\left( \frac{g(\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}-1\right) \int _{\max \{0,\bar{\tau }-a\}}^{\bar{\tau }}K(a+\theta ,\theta )\nonumber \\&\times \frac{\partial \beta }{\partial \xi }\left( \bar{\xi }(a+\theta ),\bar{S}\right) \bar{\mathcal {F}}(a+\theta )d\theta \nonumber \\&+\,\bar{b}\frac{\mu (\xi _A-,\bar{S})-\mu (\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}\int _{\max \{0,\bar{\tau }-a\}}^{\bar{\tau }}\beta (\bar{\xi }(a+\theta ),\bar{S})\nonumber \\&\times \bar{\mathcal {F}}(a+\theta )K(\bar{\tau },\theta )d\theta -\,\bar{b}\left( \frac{g(\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}-1\right) \nonumber \\&\times \,\int _{\max \{0,\bar{\tau }-a\}}^{\bar{\tau }}\beta (\bar{\xi }(a+\theta ),\bar{S})\bar{\mathcal {F}}(a+\theta ) \int _{\bar{\tau }}^{a+\theta } \frac{\partial \mu }{\partial \xi }\left( \bar{\xi }(\sigma ),\bar{S}\right) K(\sigma ,\theta ) d\sigma d\theta \nonumber \\&+\,\chi _{[0,\bar{\tau }]}(a)\bar{b}\frac{\beta (\xi _A+,\bar{S})\bar{\mathcal {F}}(\bar{\tau })}{g(\xi _A-,\bar{S})}K(\bar{\tau },\bar{\tau }-a). \end{aligned}$$
(4.31)
$$\begin{aligned} k_{22}(a)= & {} -\bar{b}\int _0^{\infty }\left\{ \gamma (\bar{\xi }(a+\theta ),\bar{S})L(a+\theta ,\theta )\right. \nonumber \\&\quad \left. +\,\frac{\partial \gamma }{\partial \xi }(\bar{\xi }(a+\theta ),\bar{S})K(a+\theta ,\theta )\bar{\mathcal {F}}(a+\theta )\right\} d\theta \nonumber \\&-\,\bar{b}\left( \frac{g(\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}-1\right) \int _{\max \{0,\bar{\tau }-a\}}^{\bar{\tau }}K(a+\theta ,\theta )\frac{\partial \gamma }{\partial \xi }\left( \bar{\xi }(a+\theta ),\bar{S}\right) \bar{\mathcal {F}}(a+\theta )d\theta \nonumber \\&-\,\bar{b}\frac{\mu (\xi _A-,\bar{S})-\mu (\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}\int _{\max \{0,\bar{\tau }-a\}}^{\bar{\tau }}\gamma (\bar{\xi }(a+\theta ),\bar{S})\bar{\mathcal {F}}(a+\theta )K(\bar{\tau },\theta )d\theta \nonumber \\&+\,\bar{b}\left( \frac{g(\xi _A+,\bar{S})}{g(\xi _A-,\bar{S})}-1\right) \int _{\max \{0,\bar{\tau }-a\}}^{\bar{\tau }}\gamma (\bar{\xi }(a+\theta ),\bar{S})\bar{\mathcal {F}}(a+\theta ) \nonumber \\&\times \int _{\bar{\tau }}^{a+\theta } \frac{\partial \mu }{\partial \xi }\left( \bar{\xi }(\sigma ),\bar{S}\right) K(\sigma ,\theta ) d\sigma d\theta \nonumber \\&-\,\chi _{[0,\bar{\tau }]}(a)\bar{b}\frac{\left( \gamma (\xi _A+,\bar{S}) -\gamma (\xi _A-,\bar{S}) \right) }{g(\xi _A-,\bar{S})}\bar{\mathcal {F}}(\bar{\tau })K(\bar{\tau },\bar{\tau }-a). \end{aligned}$$
(4.32)
We thank Philipp Getto and Julia Sánchez Sanz for discovering the mistake and pointing it out to us. We also thank Francesca Scarabel for checking the correctness of the formulas above. Moreover, we are very happy with the continuation of our work in Breda et al. (2015).
