TY - JOUR
T1 - Spreading speeds of rabies with territorial and diffusing rabid foxes
AU - Alanazi, Khalaf M.
AU - Jackiewicz, Zdzislaw
AU - Thieme, Horst R.
N1 - Funding Information:
The first author was supported by a scholarship from Northern Border University (Saudi Arabia). Acknowledgments. The authors thank Odo Diekmann for thoughtful comments that have much improved this paper and Hans Metz and an anonymous referee for useful remarks. The work of Khalaf Alanazi was supported by a scholarship from Northern Border University (Saudi Arabia).
Publisher Copyright:
© 2020 American Institute of Mathematical Sciences. All rights reserved.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - A mathematical model is formulated for the fox rabies epidemic that swept through large areas of Europe during parts of the last century. Differently from other models, both territorial and diffusing rabid foxes are included, which leads to a system of partial differential, functional differential and differential-integral equations. The system is reduced to a scalar Volterra-Hammerstein integral equation to which the theory of spreading speeds pioneered by Aronson and Weinberger is applied. The spreading speed is given by an implicit formula which involves the space-time Laplace transform of the integral kernel. This formula can be exploited to find the dependence of the spreading speed on the model ingredients, in particular on those describing the interplay between diffusing and territorial rabid foxes and on the distribution of the latent period.
AB - A mathematical model is formulated for the fox rabies epidemic that swept through large areas of Europe during parts of the last century. Differently from other models, both territorial and diffusing rabid foxes are included, which leads to a system of partial differential, functional differential and differential-integral equations. The system is reduced to a scalar Volterra-Hammerstein integral equation to which the theory of spreading speeds pioneered by Aronson and Weinberger is applied. The spreading speed is given by an implicit formula which involves the space-time Laplace transform of the integral kernel. This formula can be exploited to find the dependence of the spreading speed on the model ingredients, in particular on those describing the interplay between diffusing and territorial rabid foxes and on the distribution of the latent period.
KW - Basic reproduction number
KW - Cumulative infectious force
KW - Home-range size
KW - Latent period of arbitrarily distributed length
KW - Proportion of diffusing rabid foxes
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U2 - 10.3934/dcdsb.2019222
DO - 10.3934/dcdsb.2019222
M3 - Article
AN - SCOPUS:85083528132
SN - 1531-3492
VL - 25
SP - 2143
EP - 2183
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 6
ER -