Quiescence Generates Moving Average in a Stochastic Epidemiological Model with One Host and Two Parasites
Round 1
Reviewer 1 Report
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Comments for author File: 
Comments.pdf
Author Response
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Author Response File: Author Response.pdf
Reviewer 2 Report
The authors developed a deterministic coevolutionary model with two parasite types infecting one host type and studied analytically the LOCAL stability of the dynamical system. The authors introduced in the model quiescence. The authors also developed a stochastic version of the model to study the influence of quiescence on stochasticity of the system dynamics. They computed the steady state distribution of the parasite types and they obtained numerical solutions for the covariance matrix of the system under symmetric and asymmetric quiescence rates between parasite types.
The article is interesting, useful and well written. Some ideas and results need to be explained better before publication.
Line 108: “The parameters ϵ1 and ϵ2 are the rates of incoming migration of parasite 1 and 2 respectively from an outside compartment/population” Please explain this better in the manuscript. Why this happens. In this models which is exactly the host population?
The previous phrase seems to contradict “We assume 1) there is no free living parasite, i.e the parasite cannot live outside its host,” Please explain in the manuscript.
Line 119. “We finally introduce the parameters ϵ1 and ϵ2 to promote the coexistence of both strains at the equilibrium and to guarantee a unique steady state solution” . Please explain better in the manuscript. If the epsilons are zero then the authors claim that there is no coexistence?
Line 143. “As it may be impractical to determine the stability of matrix analytically [11], we use here the Lyapunov theorem to determine if the system is stable.” Please provide reference to the theorem. Also, emphasize the local stability analysis meaning in comparison with a global one.
The results of section 2.3 are not used later or are not well connected to the following results. Please provide a better connection of results in section 2.3 and the results of the next sections.
Line 184. "In (Figure 1), the stochastic trajectories fluctuates around the deterministic equilibrium as predict by equation (1). " Please add here the conditions related to the local stability found previously. Make the connect ion with these results.
Figure 1. I think is better to used dashed lines or other type for the deterministic cases and solid for the stochastic.
Figures. In the conclusions the authors mention the coexistence. Fig 1 is a very particular case. Please add another examples and figures where coexistence appears.
Line 190. Typo. Mater.
Line 237. "When the rate of entering quiescence stage (ρ) decreases, the variance of the number of infected individuals decreases (Eq1 versus Eq2" Is this an expected and normal results? Please comment in the manuscript a logical explanation. When rho decreases then I1 and I2 would have larger values?
Line 241. Comment on why the authors thinks this happens.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper under review provides an interesting insight into the relationship of one host species with two parasite species. The article makes a significant contribution to the understanding of interactions in communities of living organisms, in which both competitive and trophic interactions are present at the same time.
The text of the article needs to be slightly improved. Remarks:
Line 104: the continuation of the sentence begins without a paragraph and with a small letter;
Line 124: It's better to delete the sentence that duplicates the subtitle;
Line 180: The table should be titled at the top, not at the bottom; The first words in the left column must be capitalized;
Line 183, 226 and others: I don't see the point in putting literature references in double brackets;
Line 184: The link to the figure is not formatted correctly;
Lines 185 and 186: I see no reason to duplicate the text with numbers;
Lines 190-196: You may not write text that does not belong to any of the subsections of section 4. It must be given a title or included in subsection 4.1;
Line 349: There is no Conclusion section in the article; it should be added in order to look at the simulation results from a practical point of view, describing more fully the possible applications of a similar approach in practice.
The format of the bibliography is unsatisfactory:
there are no references to doi from those sources where they are definitely available (line 457, 464 and many others),
full names are given instead of Abbreviated Journal Name (lines 456, 481 and many others),
words in journal titles are capitalized (lines 456, 462, 477 and many others),
there is incorrect punctuation in most sources (lines 476 and others),
there is no editor, publishing house, city (line 484, 827 and many others),
pages are missing (lines 518 and many more),
an incomplete number of authors is given (line 496, 510, 518 and others),
it is not clear what source is mentioned (line 461 and others).
The manuscript needs careful editing. The text contains numerous technical shortcomings that are unacceptable for a mature researcher. I recommend the authors to re-edit the manuscript very carefully.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors answered the questions and improved the paper.
Author Response
Dear Authors,
Thanks for your submission.
Please make the following changes:
1) Make sure that systems are labeled with parentheses. For example 3 on line 164 should be (3), etc.
Corrected at line 164 and at several places.
2) On line 178, keep ``one of" as it was.
Corrected line 178.
3) Need some discussion on the parameter values for figures and examples. Are they hypothetical or from field study, etc.
We now state that all values are hypothetical and not based on empirical mesurements (lines-218 217)
4) What is d in P(H) of Proposition 1?
d has been replaced by e to avoid confusion, and the coefficient of the polynome are defined on pages 15 and 16.
5) Matrix N in Appendix D is not readable.
The diagonal elements of Matrix N are now explicitly written below the matrix to improve the readability.
