Understanding Neutrophil Dynamics during COVID-19 Infection
Round 1
Reviewer 1 Report
The paper is interesting and can be accepted after minor revision.
- Section 3.1. Asymptotic Analysis Results can be well organized if the more details are added. Write the equilibrium points and their existence and stability conditions as Theorems.
- How the R.H.S of inequality (6) or (8) be deduced?
- Unify the references style
Author Response
Response to Reviewer 1:
The paper is interesting and can be accepted after minor revision.
We thank the reviewer for their assessment. We carefully addressed the comments and suggestions, all of which have helped improve the quality of our paper.
Q1. Section 3.1. Asymptotic Analysis Results can be well organized if the more details are added. Write the equilibrium points and their existence and stability conditions as Theorems.
A1. We appreciate this suggestion. We restructured section 3.1 into propositions that contain conditions for the existence and asymptotic stability of equilibria. We have included detailed proofs for these conditions.
Q2. How the R.H.S of inequality (6) or (8) be deduced?
A2. Proposition one in section 3.1 now contains the derivation of conditions (6) and (8).
Q3. Unify the references style.
A3. We have carefully edited the references and citation styles to give the manuscript a unified look.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors studied a mathematical model of innate immunity following 261 SARS-CoV-2 infection that describes neutrophils recruitment into the lungs following 262 epithelial tissue damage and investigates their role in inducing disease resolution or in 263 enhancing disease pathogenesis. Although the subject of this manuscript is of interest in nowadays, I think there are a large quantities of works in studying of dynamics of COVID that are not properly cited what generates doubt about the novilty of present work.
Author Response
Response to Reviewer 2:
The authors studied a mathematical model of innate immunity following SARS-CoV-2 infection that describes neutrophils recruitment into the lungs following epithelial tissue damage and investigates their role in inducing disease resolution or in enhancing disease pathogenesis. Although the subject of this manuscript is of interest in nowadays, I think there are a large quantities of works in studying of dynamics of COVID that are not properly cited what generates doubt about the novilty of present work.
We thank the reviewer for their assessment. We have tried to include COVID-19 papers that describe the immune responses (see reference 47) but also SARS-CoV-2 viral dynamics (47-56). If the reviewer has specific works in mind, we would be happy to cite them.
Reviewer 3 Report
1. Sec. 2.1: we model the interaction between active and apoptotic neutrophils n(t) and a(t), macrophages m(t), pro-inflammatory mediators c(t), anti-inflammatory mediators g(t), and CD8 T-cells e(t) over time t, as follows. I did not see the equations that covered these parameters. How do they interact with each other? Is Figure 2 sufficient to describe them?
2. Line 114: Longitudinal average and standard deviation values for total neutrophils, CD8 T-cells, and IL-10 were collected from 27 patients with mild and 13 patients with severe COVID-19 disease at days tj ∈ T = {2, 5, 8, 11, 14, 17} post hospitalization. The mathematical model is quite complicated, with so many parameters to estimate. However, the sample size seems small. How reasonable are these estimates? Are the estimates reliable and consistent?
3. Abstract and conclusion sections: Such results can guide interventions. However, the guide was not clearly given. What are the cutoff points for the parameters to provide guidelines?
4. Figure 8: The order of the parameters is not ordinal. Take P, for example. Why not present 0.1, 1, then 10?
Comments for author File: Comments.pdf
Author Response
Response to Reviewer 3:
We thank the reviewer for their assessment. We carefully addressed the comments and suggestions, all of which have helped improve the quality of our paper.
Q1. Sec. 2.1: we model the interaction between active and apoptotic neutrophils n(t) and a(t), macrophages m(t), pro-inflammatory mediators c(t), anti-inflammatory mediators g(t), and CD8 T-cells e(t) over time t, as follows. I did not see the equations that covered these parameters. How do they interact with each other? Is Figure 2 sufficient to describe them?
A1. The system of equations governing the interactions between these variables is equation (3), and indeed it is based on the diagram in Figure 2.
Q2. Line 114: Longitudinal average and standard deviation values for total neutrophils, CD8 T-cells, and IL-10 were collected from 27 patients with mild and 13 patients with severe COVID-19 disease at days tj ∈ T = {2, 5, 8, 11, 14, 17} post hospitalization. The mathematical model is quite complicated, with so many parameters to estimate. However, the sample size seems small. How reasonable are these estimates? Are the estimates reliable and consistent?
A2. The reviewer is correct that with the sparsity of data we cannot have great confidence in estimating many parameters. That is why we restricted our fitting to just four and assumed the others known (from literature). Even with the four estimates, we further analyzed the uncertainty by computing local sensitivity analyses for each of the four parameters. We believe the parameters are representative for the data presented in the study.
Q3. Abstract and conclusion sections: Such results can guide interventions. However, the guide was not clearly given. What are the cutoff points for the parameters to provide guidelines?
A3. The guidelines do not come from the parameter estimates, but rather from the different dynamics observed in mild versus severe cases. We have removed the ‘guide interventions’ from abstract and conclusion.
Q4. Figure 8: The order of the parameters is not ordinal. Take P, for example. Why not present 0.1, 1, then 10?
A4. We thank the reviewer for pointing out the lack of order in the parameter values. We have fixed that in the caption of figure 8.
