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Required Reviews Completed Ê®ÎåÌì
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ÕâÊÇÖ÷±à¸øÎҵĻØÐÅ£¬¸½Á˵ÚÒ»¸öreviewerµÄÒâ¼û£º

Dear Mr. Wu ,

I have now received the referees' reports on your paper, from which you will see that, although they are broadly supportive of publication, this is conditional on your addressing the criticisms they have made.

Please carefully address the issues raised in the comments.
If you are submitting a revised manuscript, please also:
a) outline each change made (point by point) as raised in the reviewer comments   
  AND/OR
b) provide a suitable rebuttal to each reviewer comment not addressed

To submit your revision, please do the following:
1. Go to: http://ees.elsevier.com/apm/
2. Enter your login details
3. Click [Author Login]
This takes you to the Author Main Menu.
4. Click [Submissions Needing Revision]

I look forward to receiving your revised manuscript.

Yours sincerely,

M. Cross
Editor
Applied Mathematical Modelling

Reviewers' comments:

Reviewer #1:
page 1:
The idea of invasion-speed calculations: see also Daniels75,
Mollison72, and the initial work of Fisher and Kolmogorov.
page 2:
The reproduction kernel postulates instantaneous dispersal
between locations.  For a discussion of similar scalar
models see Medlock and Kot, 2003.  
page 3:
In this model (1.3), the delay is equivalent to
age-structure, which probably has been studied previously in
this context.  Implicit use, for instance, is made in Reluga
et al 06.

The connection between the model and epidemic spread is
tenuous.  There is no obvious reason why infected
individuals would spontaneously transmit a disease to
a new location on time scales faster than the diffusion rate
d while still requiring infected individuals to stay in one
place.  Additionally, as you point out, the assumption that
g() is independent of u_2 is only valid early in an epidemic
when susceptible population size is unaffected, and it's not
clear exactly when epidemiology mechanisms are implied by
the current form of g().  However, there may be other
biological situations where this invasion model is useful,
so the results are still valuable.  For now, either downplay
the epidemiology connection or provide a justification from
first-principles for a specific disease.

paragraph 2, "the the" -> "the"

section 2, in the definition of c*, you need a localized
initial condition, and it's probably better to only require
u(t,x) \geq \hat{u} rather than strict equality since some
models exhibit oscillations or unbounded growth.

page 4: define quasi-monotone in this context.
I found the order of the calculations used to reach eq 2.9
a little confusing.  The k's, for instance, were introduced
too soon.

Please provide a reference for the origin of the ideas used
to reach 2.13

page 8, line -2: sentence is confusing
page 9, line 4 "an decreasing" -> a decreasing

----------- References -------------------

title={The Deterministic Spread of a Simple Epidemic},
author={H. E. Daniels},
booktitle={Perspectives in Probability and Statistics :
Papers in Honour of {M. S. Bartlett} on the Occasion of his
Sixty-Fifth Birthday},
editor={J. Gani},
publisher={Academic Press},
address={London},
year=1975,
pages={373-386},
     
author = {D. Mollison},
title = {The rate of spatial propagation of simple epidemics},
booktitle = {Proceedings of the 6th Berkeley Symposium on
Mathematical Statistics and Probability},
publisher = {University of California Press},
year = {1972},
volume = {3},
pages = {579-614},
address = {Berkeley, CA},

author = {R. A. Fisher},
title = {The wave of advance of advantageous genes},
journal = {Annals of Eugenics},
year = {1937},
volume = {7},
pages = {353-369},

author = {A. Komogorov and I. Petrovsky and N. Piscounoff},
title = {Etude de l'equation de la diffusion aved croissance de la quantite
de matiere et son application a un prbleme biologique},
journal = {Moscow University, Bulletin of Mathematics},
year = {1937},
volume = {1},
pages = {1-125},

title={A Model of Spatial Epidemic Spread When Individuals Move Within Overlapping Home Ranges},
author={T. Reluga and J. Medlock and A. Galvani},
journal={Bulletin of Mathematical Biology},
year=2006,
volume=68,
pages={401-416},

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