Longitudinal Projection of Herd Prevalence of Influenza A(H1N1)pdm09 Virus Infection in the Norwegian Pig Population by Discrete-Time Markov Chain Modelling

Round 1

Reviewer 1 Report

This is a well written, concise draft that looked at the forecasting power of the Discrete Time Markov’s Chain (DTMC) to predict with significant level of accuracy, at least for the first few years and based on good surveillance data availability. By using serological data of the influenza A(H1N1)pdm09 virus (H1N1pdm09) infection in pig population collected during the Norwegian active surveillance between September 2009 and 2020, the authors showed that DTMC can significantly predict the infection trends of H1N1pdm09 between 2009 and 2016, showing a high prevalence corelation between the DTMC model result and real-time prevalence. However, this predictive power and correlation disappeared from 2016 onwards. The authors  conclude by describing the potential usefulness of DTMC as a predictive tool for detecting, estimating, and possibly managing the effect of exotic outbreaks by animal health authorities around the world to reduce loss. Although this is a greatly well-presented work, I have made some suggestions for possible improvement.

Minor

1. Line 10: Please provide the full description of OIE as this is the first time it is appearing in the text.
2. Line 101: Did you mean to IAV? Please correct.
3. Line 102: "antibodies and followed by the haemagglutination" reads better as follows "...antibodies followed by the haemagglutination".
4. Line 101: "...as the probability of a pig herd " reads better as follows "...as the probability that a pig herd".
5. Line 225: disease

Major

1. Discussion: The other model of disease trends available such as the SIR/SEIR and Growth (logistic and exponential) modes provide a more comprehensive analysis of disease trends as they incorporate various aspects of the disease dynamics. Thus, the drop in the predictive effect from 2016 will most likely be associated with some undiscussed or undetected factors.

Could you thus do more research and provide possible explanations for this drop. For instance, has the sero-surveillance periods (time of the year when samples are taken), type of antibody etc tests or the treatment or management (of animals or farms) system changed recently. The aim will be to detect in real-time the factors responsible for this drop in predictive power.

2. As also part of the first major points, this discussion aspect did not include the possible limitations of this technique and how it performs in the context of previous works both using the DTMC or other models to predict disease infection trends in animals around the globe and why this method should be used etc. in summary the discussion section should be expanded with due reference and recognition of previous works in the field and provide a context by comparing this method to others that have be used in similar scenarios.

Author Response

Please see the attachment. 

Author Response File: Author Response.pdf

Reviewer 2 Report

 The manuscript “Longitudinal projection of herd prevalence of influenza A(H1N1)pdm09 virus infection in the Norwegian pig population by discrete-time Markov chain to estimate future disease burden” is a retrospective study presenting the efficacy of discrete-time Markov chain in forecasting possible pig herd prevalence of H1N1pdm09 with a one-year interval as a time step. This study was conducted in Norway for ten years.

Given the complexity involved, the author has produced many positive and welcome outcomes. Overall, this research is well written, and the content of this manuscript is of major interest. Nevertheless, the following issues need to be addressed:

Lines 9-10: This sentence should be rephrased. “In 2009…” and then “on 30 September 2009” is redundant.

Line 20: I would add a last (conclusive) sentence at the end of the abstract. For instance, you can write a sentence similar to that in lines 27-30.

Lines 39-42: This sentence is too large and hard to follow. Please rewrite it.

Line 42: Please define the abbreviation “WHO”

Line 93: Why the title of MM is in blue?

Please check the whole text for typographical mistakes (spaces, no spaces between the words…..)

The paper would be significantly improved with the addition of some changes in the discussion.

The reference list style is wrong

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The purpose of the paper was to develop the two-state discrete-time Markov chain (DTMC) using transition probability matrices as a tool to capture H1N1pdm09 virus infection dynamics in pig population. 

From a mathematical point of view, the paper presents a simple (one might say, naive) application of the method, but I still think that the paper will find its readers and therefore I recommend it for publication if the following comments and suggestions will be taken into account in the revised version. However, I have serious doubts that this will be possible within the framework provided by this work, that is, that the present state fully captures all the information that could influence the future evolution of the process, which is the essence of the DTMC approach. 

English is in some places at a rather weak level and impairs the readability of the work. 

Specific (major) comments and suggestions:

1) Page 7 - Figure 2: The difference between the observed (P) and possible (P^) prevalence after the year 2016 indicates that the model you created is not very accurate(= does not correspond with the observed data) and, in my opinion, the model is not applicable in its current form and needs to be improved! 

2) Line 175 as well as lines before: Using the letters "p" and "P" (for the prevalence, probability and transition matrix) and their versions with "^" cause problems in understanding the text. For example, for probability could be used Pr (Lines 149-150). See also the line 175, where small letter p and capital letter P are used for the same.

Specific (minor) comments and suggestions:

3) Lines 28-29: This sentence is difficult to understand and should be reworded;

4) Line 118: Should be 1x2 matrix [p,q] (or -> a row vector [p,q]); square brackets [ ] are used at the line 149;

5) Line 150: Missing the dot at the end of line;

6) Line 151: typo -> "this chain as the following form";

7) Line 173: "three coloumns" should be "three columns";

8) Line 301: "1." should be removed.

Author Response

Please see the attachment. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Dear Authors,

To the best of my knowledge this  is an insightful work providing alternative method  for the crude prediction of the trends and dynamics of infectious diseases in farm animals.

I am happy with the manuscript in its current form.

Best Wishes

Author Response

Thank you for your kind comments. 

I have resubmitted a version now that has tracked changes (mostly language and grammar corrections).

Regards

Er Jwee Chiek

190821

Reviewer 3 Report

My main concern raised in the comments on the earlier draft, namely,

"Page 7 - Figure 2 (now Page 8 - Figure 3): The difference between the observed (P) and possible (P^) prevalence after the year 2016 indicates that the model you created is not very accurate(= does not correspond with the observed data) and, in my opinion, the model is not applicable in its current form and needs to be improved!" is not reflected in this revised version of the manuscript. 

The extended discussion on the pages 9-10 does not solve the problem of mathematical modeling. I consider the publishing of such work as problematic, but not excluded, also given that the author himself draws attention to the shortcomings of the mathematical model (and possible causes). 

I recommend publishing this article after fixing formatting errors and problems in grammar, punctuation, and sentence structure. 

Line 278: "dyanmics"

Line 282: "dynmaics"

Author Response

Thank you for your kind and useful comments. 

The model indeed is not good enough for extended prediction of the pig herd prevalence. I have now highlighted that the predicted value of the model is good only for the first seven years. I believe this initial phase of seven years may be useful for health authorities to estimate the initial disease burden and make animal health /human health economic evaluations already. 

As to the mathematics of the model, I have used the initial initial prevalence estimated in 2009 as the vector prevalence. I have used the two year consecutive surveillance data on incidence and recovery to extract the probabilities for the fixed transition matrix.  I am unsure how else I should approach in constructing the DTMC model. 

I have corrected the spelling error on "dynamics" and made quite a few language changes to the make the article more readable. The resubmitted article has tracked changes and so you can see the changes I have made. 

Regards

Er Jwee Chiek