An Age-Distributed Immuno-Epidemiological Model with Information-Based Vaccination Decision
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsSee the attached file
Comments for author File: 
Comments.pdf
Author Response
Please find the attached response file.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors#Please consider the attached file.
Comments for author File: Comments.pdf
#The entire manuscript should be carefully proofread for grammatical, typographical, and punctuation errors.
Author Response
Please find the attached response file.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors have developed an age-distributed immuno-epidemiological model incorporating information-based vaccination behavior. The model extended prior approaches with distributed recovery and death rates and includes an information index affecting vaccination uptake. The authors derived analytical expressions for the basic reproduction number R_0 and bounds for the final epidemic size for a reduced model without age structure. The full age-distributed model's well-posedness has been proved via a Banach fixed-point argument. Numerical simulations explored the influence of memory kernels, vaccine effectiveness, and behavioral parameters on epidemic trajectories.
The topic is timely and relevant to mathematical epidemiology, particularly in understanding behavior-driven vaccination during outbreaks.
My comments are:
1) The authors introduced a mathematically rich age-distributed model (Section 2), but all analytical work and simulations focus on the reduced age-independent version.
While the age-structured system is rigorously formulated and its solvability proven, it is never simulated nor compared to the reduced model. This weakens the motivation for developing the age-structured model in the first place. Include at least one numerical experiment demonstrating differences between age-distributed and age-independent outcomes.
2) The information index mb(t) (page 15) depends exclusively on the infected population, yet real vaccine behavior is influenced by multiple factors. Why using incidence alone is a reasonable proxy, or compare with an alternative formulation using hospitalizations or risk perception.
3) Figures in Section 4 clearly show sensitivity to memory decay, but there is no analytical explanation of why short-term memory yields better control.
4) The paper lacks some more discussion on recent works of mathematical biology such as:
a) Bifurcation and control of a predator-prey system with two time delays
b) Combination-combination synchronization and ultimate bound of the fractional-order ecological system
c) Dynamics exploration for a fractional-order delayed zooplankton– phytoplankton system
5) The paper contains many hyphenation artifacts such as “in￾fected” and “progres￾sion.” These should be removed throughout.
6) Page 4: “impact of vaccination decision on the epidemic outbreaks.” → “decisions”
7) Page 15: “does not depend on parameters and on the kernel type” → revise to “does not depend on the parameters or on the kernel type.”
8) Ensure consistent formatting of m_b, ρ_b, and other subscripts.
9) Some equations in Section 3 have missing parentheses that make expressions difficult to parse (e.g., eqs. 17 and 19).
10) Figures 2–4 have small axis labels; increasing font size would improve readability.
Author Response
Please find the attached response file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper can be published
Author Response
Thank you for accepting the paper.
Reviewer 2 Report
Comments and Suggestions for Authors#Please consider the attached file.
Comments for author File: Comments.pdf
Author Response
The grid lines are removed in Figure 11. Thank you.
Reviewer 3 Report
Comments and Suggestions for AuthorsAccept
Author Response
Thank you for accepting the paper.
