General Comments:

I like the idea of having a section describing the data, and
another describing the methods.  I was a little confused about the
exact form of the data, and what the errors in data collection were.
The descriptions of the models were very clear.  I think it would be
nice to have a more explicit description of what happens when you move
to a multivariate ARIMA model, which you seemed to do for the SIR models.

Section 2:
Summary of what I took away from section 2:

I think you are trying to describe exactly where the data is coming
from and what the form of the data is.  You say PAHO gives "cumulative
counts", for all countries, but I'm not exactly sure what they are
cumulative counts of.  There seems to be some data collection error
resulting in negative cases, which is clearly impossible, but I didn't
fully undestand the chain of how negatives can happen.


Specific Comments:

1st paragraph, last sentence,  "In addition to..."

I think clarifying what a "count" is would help the reader understand
what specifically the data is.  I was not sure if the count they
report is a count of new cases or a count of currently infected
individuals.  

You also use the word "transmissions" and I wasn't sure if
transmissions are the same as "counts" or different.  If they are the
same, use the same word for consistency, and otherwise define it
explicitly.

Both of these changes are to help with the problem of synonyms and
distant background bfrom Lebrun pp. 10-11.  If the definition isn't
explicit I make up one that I think is correct, but may not be.

2nd paragraph, first sentence:

Here you use the phrase "cumulative counts", and I'm not sure if this
is the same counts from before.  Again defining one phrase early and
being consistent will help here.



Section 3:
Summary of what I took away from section 3:

You are proposing three different methods to model the evolution of
the Chickungunya infection.  The SIR model, the SIR mosquito model,
and the ARIMA model.  The SIR models are based on differential
equations relating the S, I, and R compartments, while the ARIMA is
based on a time series approach.  Unfortunately, you cannot use the
mosquito model without further data about the mosquito populations in
the countries.


Specific Comments:

Can you make Section 3 begin on a new page, the figure in between made
it particularly difficult to read the second sentence of section 3.

Paragraph 1:

I found it distracting when you mentioned sections 3.1 and 3.3,
because I immediately started thinking "why is 3.2 skipped".  This
makes me think of the idea of Gopen and Swan that you should minimize
distractions to the reader.

Paragraph 1, sentence 1:

Since you are going to describe three models, maybe you can say "We
propose three models for describing the number of infected cases of
Chikungunya."  This sets me up to not be surprised by the introduciton
of the third model later on.  I think you can wait until the next few
sentences to actually name the models.  This sentence seems to be
scaffolding a little bit, but I think some introduction is useful for
the reader.

Paragraph 1, rest of paragraph:  You tell us here which sections
describe two of the models, but give short descriptions of each
later.  I think you can instead spend a sentence for each model, and
then say where it is described.  Something like:

"The first model we propose is the SIR compartment model which we
describe in section 3.1.  We then propose an extension of the SIR
model which acccounts for the mosquito population that transmits the
disease in section 3.2.  Lastly, we propose an ARIMA model of
infection in section 3.3."

This construction guarantees one idea per sentence, as Gopen and Swan
would suggest, and also keep the models in the order you present them,
which I think makes a lot of sense given the connection between the
two SIR models.

Paragraph 2:

there seem to be four main ideas here:

1)  We account for people travelling between countries in our SIR
model
2)  We account for different countries using a different SIR model for
each country.
3)  We use the minimizer of SSE to estimate parameters
4)  We have data on flight itineraries to estimate movement between
countries, but we have to estimate it as a constant due to data
constraints.

I think pointing out idea 1 here is good, so the reader knows what to
expect going forward, but I think the specifics of idea 2 can be held
for section 3.1, where you already have a good explanation of how you
extend the SIR to multiple countries.  I also think idea 3 should be
moved to section 3.1.  It seems out of place here before I have seen
what the model looks like.

All of these moves will help give the
paper the "hour glass" shape talked about in Bem, where the casual
reader will know the basics of what your method does, but the
specifics are saved for a later section.

Idea 4, flight itenerary data:

I think this information could be moved to section 2, so that you have
all the specifics of your data together in one section.

Section 3, paragraph 3:

This paragraph gives some specifics on how the ARIMA model deals with
multiple countries, but I again think you could save the specifics for
section 3.3 where you go over the model.

I would consider removing this paragraph, and mentioning after the
short model descriptions that the models you propose all have ways of
dealing with the multi-country data that you have available.


Section 3.1:

I really like this section, and I think it explains the model very
well.

I would add to this section some information about choosing the
parameters that minimize the SSE.  For instance, you can state exactly
what SSE you are minimizing, and what parameters you are estimating.

Section 3.2:

I also think the description in this seciton reads really well.

I was wondering why the parameter a is not indexed by country, but b
and c are indexed by country.  Does this mean the biting rate is constant, but
the transmission probability is different from country to country?  If
this is the case, it might be useful to mention why that's a
reasonable assumption, that way the reader doesn't get distracted
wondering what is going on here.

Section 3.3:


You were very explicit in sections 3.1 and 3.2 about how you are
extending the univariate models to deal with multiple countries.
Would it be possible to say more about the multivariate models in this
section?

Equations 5 and 6:  You  use i as an index here, which before was
indexing countries, could you use a different index, maybe r or s?
This change is relatively minor, but for consistency it could help the
reader not confuse what is being indexed.