Optimal Voluntary Vaccination of Adults and Adolescents Can Help Eradicate Hepatitis B in China

Round 1

Reviewer 1 Report

This is a study that builds a theoretical disease model and game theory model to evaluate how voluntary vaccination might affect Hepatitis B eradication in China.  The theoretical results are interesting, but, I still have some questions and concerns.

1. My first comment is about the cost of chronic HBV treatment. The authors say, “Recent studies of the cost-effectiveness of available treatments for chronic HBV indicate that antiviral therapies impose a significant financial burden on patients, and the drugs with the highest efficacies are priced out of reach of the average Chinese adult 63 [59, 62]”

However, the costs of generic entecavir and tenofovir have dramatically dropped by about an order of magnitude since those studies were published.  That has made chronic HBV treatment with highly efficacious drugs much more cost-effective (and, likely more affordable).

For example, see:

Toy M, Hutton D, McCulloch K, Romero N, Revill PA, Penicaud MC, So S, Cowie BC. The price tag of a potential cure for chronic hepatitis B infection: A cost threshold analysis for USA, China and Australia. Liver International. 2021 Jul 30.

If identified, antiviral treatment might be less than $50 per year.  Of course, adding in other monitoring costs etc would add the annual costs.  But, in the end, the net present value of the costs of someone on treatment might be on the order of a few thousand dollars rather than $40,000.

I would think this could alter the K value of the relative cost of infection.  That might then change some of the conclusions.  It also might suggest the costs of vaccination might have to be reduced even more in order to encourage vaccination.

2. My next comment relates to the inclusion of age. As the authors note, age can be very important in terms of infection risk and in particular, risk of an infection becoming chronic. However, age is not in this model.  To what extent might this be a problem for you?
3. I have some questions about vaccine effectiveness and waning. The 12% vaccination failure (citation 33) appears to be based on vaccination titers observed. However, the cited study also says, “Throughout this publication, seroprotection against hepatitis B is therefore defined as titer higher than 10 mIU/ml. Recent publications, however, show that individuals with non-zero anti-HBs levels show an anamnestic response to a challenge dose and indicate the persistence of immune memory to HBsAg even when anti-HBs are well below the estimated protective threshold.” Also, given that, is a 30-year mean duration of protection realistic? (citation 53).  I realize there is a lot of uncertainty surrounding this parameter.
4. The assumption is 100% vaccination at birth. If so, how would people know they don’t have vaccine protection? Presumably, they would have to know their vaccine protection had sufficiently waned. How do people know to get (re)vaccinated?
5. I have some questions about the decision makers in the game theory model. Does the patient pay the costs of the vaccine and disease? OR are there costs that an insurance company or government pays?  That might affect some of the costs that the decision-maker faces.  It might be good to highlight that more.
6. I have some questions about the formulations of the probabilities of infection. Are the probabilities in equations 9 and 10 (and 12 and 13) per year? Or lifetime?
7. In the conclusions/discussion, there is a statement, “Our results show that given the success of current efforts to inoculate children [33], population-level herd immunity against HBV can be obtained through annual vaccination of approximately 11% adults and teens”. I would rephrase this to say “who are susceptible” at the end of this sentence.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

It is an exciting application of game theory, very well written. There are great policy suggestions and recommendations. 

• The title feels more like a response to a research question, and please review and modify it.
• The authors state in lines 64-65, “There are now many mathematical models of HBV dynamics, see for example [32].” If there are many, why do you only cite one of them? Please quote others accordingly.
• The authors discussed the motivation very nicely, but I can’t seem to find the gap and clearly see the research question here. Please state your research question closer to the end of the introduction to tell your reader what the problem is you are trying to solve.
• Please put line 115 closer to your figure (right below or above).
• Line 126, are π_{ν and ^πnν} representing the same thing? It isn’t very clear, and please clarify.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors propose a model based on the set of dynamical equations of epidemic model for hepatitis B disease. Many recent studies have been devoted to the game theoretical based epidemic model. The current structure of the manuscript does not do an outstanding job in giving a comprehensive and novelty of this field of research. The authors should do better in this regard. Current work only emphasized theoretical development and analysis, which may not sound so attractive to general readers. The author should include more numerical analysis, and explanations about every parameter variation. I believe that authors should introduce several extra details before resubmitting  this manuscript. Also, authors should read more pieces of literature which are relevant to the current study. After reading the works of literature, the author should explore more explanations by adding a new result and discussion section in the body text.

For example:

To vaccinate or not to vaccinate: A comprehensive study of vaccination-subsidizing policies with multi-agent simulations and mean-field modeling, Journal of Theoretical Biology 469, 107-126, 2019.

Evolutionary game theory modelling to represent the behavioural dynamics of economic shutdowns and shield immunity in the COVID-19 pandemic. R. Soc. Open Sci. 7: 201095. http://dx.doi.org/10.1098/rsos.201095 (2020).

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I am satisfied with the authors' responses to my comments.

Reviewer 3 Report

Current form of Manuscript is acceptable.