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Thank you for making the requested changes to your manuscript.
[# PeerJ Staff Note - this decision was reviewed and approved by Jun Chen, a PeerJ Section Editor covering this Section #]
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The quality of the manuscript has significantly improved and more comprehensive after the revision, especially by including more countrys and longer time in the modeling.
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The manuscript has bee revised in the light of the reviewers comments and the clarity of the message much improved. The findings remain valid and the links to mechanistic models set the work solidly in context. The simplicity of the model and language make the manuscript accessible to those making policy decisions around new outbreaks of disease.
Your manuscript elicited a wide range of opinions about its validity, especially about the appropriateness and the simplicity of the models you selected. Although you will need to respond to all the author comments in detail, here are ones that I want to particularly highlight:
1. You need to better explain how interventions affect models, and justify your choices of r and alpha. This means tying in the mathematical components of your models with the actual epidemiologic importance of them.
2. Add other countries (South Korea, Singapore), and address where model does not do an effective job. One reviewer indicated that your models do not work well for South Korea. If this is true, then this should be explored and explained, as it is important to know under what circumstances (and countries) the models do and do not predict mortality well.
3. One reviewer made this important comment: "Their mathematical models (the Richards growth model (RGM) and generalized growth model) are too simple to capture country-specific COVID-19 transmission dynamics and also country-specific fatalities in the five countries." Please provide a strong justification for your models in addressing this comment, because interventions will be country-specific, so models should be specific to countries.
4. Another reviewer wrote: "This is a basic exercise in curve fitting and does not provide any insight to the nature of the epidemic. Since it is a phenomenological model, it is very strange to interpret a change in parameters as interventions. Interventions should modify the mechanisms of disease spread in certain ways, but such mechanisms are not considered here. Even worse, in reality there were a sequence of progressively applied interventions in each of the considered countries." Again, your models should be more than curve-fitting exercises, so it will be important to integrate the epidemiology into the statistical models. Otherwise, your models will be exercises into historic curve fitting, but will not help predict how interventions can affect future mortality in countries.
[# PeerJ Staff Note: Please ensure that all review comments are addressed in a rebuttal letter and any edits or clarifications mentioned in the letter are also inserted into the revised manuscript where appropriate. It is a common mistake to address reviewer questions in the rebuttal letter but not in the revised manuscript. If a reviewer raised a question then your readers will probably have the same question so you should ensure that the manuscript can stand alone without the rebuttal letter. Directions on how to prepare a rebuttal letter can be found at: https://peerj.com/benefits/academic-rebuttal-letters/ #]
The paper is well written and presented.
The authors fit Richard's model to cumulative death data of COVID-19. This is a rather flexible family of curves that can be fitted to practically any sigmoid curve, and cumulative epidemic data often (but not always) have a sigmoid shape.
This is a basic exercise in curve fitting and does not provide any insight to the nature of the epidemic. Since it is a phenomenological model, it is very strange to interpret a change in parameters as interventions. Interventions should modify the mechanisms of disease spread in certain ways, but such mechanisms are not considered here. Even worse, in reality there were a sequence of progressively applied interventions in each of the considered countries.
There are no real scientific findings in this article. The Richard's model spectaculartly fails on Korean data (which was not presented here).
I find the basic reporting of the study to be very descriptive and realistic. It made
me feel that I had a good understanding of what was going to be examined. The language of writing is easy to understand even to the audience outside computational/mathematical modeling field.
It's interesting to see the modeling the COVID-19 development of several countries in different stages, including China, Italy and Iran, which brings a nice selection of target subjects.
I believe it would be also reasonable if you could include more countries like Singapore and/or South Korea, especially in the "intervention" part of the experiment, as these countries have taken relevant approaches to control the virus situation
I believe that the findings are valid, but the further significance needs to be considered. Is there existing experiments with similar approaches, in dealing with COVID-19 or even non-COVID-19 respiratory infectious disease like influenza? From my point of view, an extra content comparing the current research with other relevant modelings of respiratory infectious disease would be of great help to shed light to the community fighting against the COVID-19.
The current manuscript described the of establishment of a mathematical/computational model of the COVID-19 in aspects of fatality and how it respond to interventional strategies. I believe it's a well written article and it follows nicely to the scope of PeerJ journal publication. The topic is interesting and it could help improve the understanding of the disease development and provide sights to prevention and responding measures. I believe the the submission would be of significance to the community fighting against COVID-19, and how helps draw the attention of disease/disaster response community to the computer science and simulation world.
The paper follows a format close to the Standard structure, there is a background section but no Introduction replaced with a Background section and the materials section replaced with a section data. It might be worth reverting to having an introduction rather than background section to emphasise the point that this paper is about assessing interventions rather than predicting the course of specific outbreaks and that those fits are designed to validate the use of the RGM. In general, however, the structure is logical and clear, the language is approachable and appropriated, there are sufficient references.
The figures are reasonable, though the use of blue and red will make it difficult for those who need to print and view the papers in black and white. Using colours which have different intensities or different line types or widths, or symbols might help with this.
The raw data has been supplied and the code is correct.
Line 85 – confirmed deaths are more reliable, but “much more reliable” is a strong statement and would need some justification, particularly given that the discussion suggests that timing is critical and there are known to be variable delays in the reporting of deaths
Whilst based on a mathematical model, the focus of the manuscript is on the use of that model to investigate interventions into a pandemic thus it fits well with the scope of the journal. The subject is topical and the research timely. The algebra and code are correct and the model is well described in plain and comprehensible language.
In terms of interventions, there are two aims: to reduce the speed of an epidemic (or flatten the curve) and to reduce the size (total number of cases). This manuscript covers the second type of intervention and it would be helpful if this distinction were highlighted.
Line 111 & Equation 8 Given that a dash is being used to denote post-intervention parameters, it might be clearer to use a dot to denote differentials.
It’s a small point, but efficiency is referred to as a proportion in the text but displayed as a percentage. It would be helpful to pick one and stick with it.
Line 146 The fit to the data from China as published on 1 April is excellent, but they have just revised the death toll up by almost 50%. The authors state that purpose of these fits is simply to establish the RGM as a reasonable model for the progression of the disease rather than as a predictive tool, so this change doesn’t impact the validity of the findings, but in order to forestall misreporting of the paper it would be helpful to have that made clearer in the discussion of the paper.
Whilst the algebra is correct, it seems counter-intuitive that increasing the intrinsic rate of increase (r) leads to greater efficiency and it would be helpful to see some discussion of what is occurring here.
Line 193 & 199 It would be helpful to have some justification for the parameters chosen for r and alpha in figure 4 because alpha has values that differ by 0.6 and r has values that differ by 0.1. The statement that altering alpha has a greater effect is hard to justify given the disparity between the ranges of values tested. The rationale behind the choices made and for the comparisons really needs to be explained.
Line 218: The authors state that there is a narrow window for interventions to be effective. This is a strong statement and rather implies a cut off time whereas the model supports a statement about effectiveness tailing off. Rapidity is a judgement call and it would be more useful to discuss the timescale of efficiency reduction than a strong but somewhat vague statement.
Figure 4 would be improved by combining all lines onto one graph and representing the mitigation and suppression strategies with a different line type. It appears to represent and interesting point that even right at the beginning of an outbreak when, r is considered to dominate the dynamics, a strategy of suppression appears to have more effect.
This is a timely and helpful manuscript which uses a well understood model to look at how interventions with different effects on the spread of the disease might affect the total number of cases in a pandemic outbreak. There is no suggestion as to what the interventions might be, but the model serves to highlight what outcomes should be sought. The methods are clearly described as are the implications. The authors make some fairly strong claims and these need further justification as described above.
Authors conducted a simulation study on “Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies”. They employed two simple mathematical models and fitted to fatality data in order to investigate the characteristics of fatality curves of COVID-19 and the effectiveness of intervention strategies in five different countries; China, Italy, Spain, Iran, and Brazil. Their study can provide a critical/useful tool for the effectiveness analysis of emerging infectious diseases like COVID-19. However, some critical points from mathematical and epidemiological aspects should be considered for publication in PeerJ.
They used the Richards growth model for China, Italy, Spain, and Iran and the generalized growth model for Brazil (the early stage of epidemics).
Their mathematical models (the Richards growth model (RGM) and generalized growth model) are too simple to capture country-specific COVID-19 transmission dynamics and also country-specific fatalities in the five countries. A mathematical model should be novel enough to explain country-specific confirmed cases and fatality cases. The characteristics of key components in transmission dynamics of COVID-19 should be distinct in each country; for example, population structure (age, ethnic ratios, etc), transmissions (social interactions, clustering etc), interventions (medical infra structures etc), epidemiological features (incubation, infectious periods etc) are very distinct.
Authors should further investigate clear relations between infected (confirmed) cases and fatality cases (again, country-specific analysis should be done). The impacts of Interventions such as social distancing, quarantine and intensive treatment (hospitalized) are different on infected cases and fatality cases. This issue also needs to be validated as well. Therefore, it is insufficient for the validity of the epidemic outputs based on the two models the authors suggested. Therefore, the authors should clearly state significant contributions of epidemiological aspects using proper mathematical models.
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