Optimal allocation of resources to healthcare workers or the general populace: a modelling study

We consider a model that distinguishes susceptible; infected, but not yet infectious; pre-symptomatic, symptomatic, asymptomatic, and hospitalized infectious; recovered and dead members of two groups: healthcare workers (HCW) and members of the community that they serve. Because of the frequency or duration of their exposures to SARS-CoV-2, a greater fraction of HCW would experience severe COVID-19 symptoms that require medical care, which reduces mortality rates, absent personal protective equipment (PPE). While N95 masks (and, possibly, other scarce medical resources) are available to members of both groups, they do not use them equally well (i.e. efficacy and compliance differ). We investigated the optimal allocation of potentially scarce medical resources between these groups to control the pandemic and reduce overall infections and mortality via derivation and analysis of expressions for the reproduction numbers and final size. We also simulated prevalence and cumulative incidence, quantities relevant to surge capacity and population immunity, respectively. We found that, under realistic conditions, the optimal allocation is virtually or entirely to HCW, but that allocation of surplus masks and other medical resources to members of the general community also reduces infections and deaths.


Comments to the Author(s)
The submitted paper was well written and some interesting results concerning the COVID-19 control have been provided, I do suggest that this paper could be accepted for publication RSOS.

Review form: Reviewer 2
Is the manuscript scientifically sound in its present form? Yes

Are the interpretations and conclusions justified by the results? Yes
Is the language acceptable? Yes

Recommendation? Accept with minor revision (please list in comments)
Comments to the Author(s) Comment on Manucript_RSOS-210823 In this manuscript, the authors developed an ODEs system consisting of two groups (HCW and members of the community) and investigated the optimal allocation of potentially scarce medical resources between these two groups to control the pandemic. The manuscript overall is wellwritten, and the methods and findings are illustrated with clear details. However, some concerns can be addressed to increase clarification: 1.
My main concern is about the model setting. Many studies have studied the transmission of diseases in a hospital setting (e.g., https://doi.org/10. 1098/rsos.201895; https://doi.org/10.1371/journal.pone.0030170; doi:10.3934/mbe.2019181; doi: 10.3934/mbe.2015.12.761https://doi.org/10.1016/j.mbs.2019.01.013) that the three main causes for HCW infections are due to 1. HCW-to-HCW contacts; 2 HCW-to-Patient contacts; 3, environmental contamination. For the specialty of COVID-19, I am ok to consider HCW-tofriends/family/neighbors/other members of the community contact. But please clarify why you ignore patients (as another important group) if you try to control the infections for HCWs, since in my view if you ignore patients, you will greatly decrease the risk of HCWs. Is it a better idea to consider HCWs, patients, and other communities? Please clarify.

2.
The authors used both the reproduction number and final size as measurements for control of the disease for different allocation strategies. As we know, the population of HCWs is relatively small compared to the general community). The final size F=F1+F2=Z1/N (the fraction of HCWs) +Z2/N(the fraction of community) is not fair to use since even though all HCWs are infected, F value can't be reflected dramatically. I would suggest using both F1 and F2 respectively to indicate the control of the disease since it is a big deal if the hospital's system is ruined by pandemics (e.g., most HCWs get infections). So it goes back to my #1 concern, please clarify the model set.

3.
For table 1, it is best to have another column to indicate the source/reference of your parameter values even though in the text you mentioned some reference there.

4.
For figure 3, I think you showed the result for Optimal strategies B and C. Please change your figure legend (A with % HCW; B with % HCW) to B and C.
Decision letter (RSOS-210823.R0) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Feng
On behalf of the Editors, we are pleased to inform you that your Manuscript RSOS-210823 "Optimal allocation of resources to health care workers or the general populace: a modeling study" has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referees' reports. Please find the referees' comments along with any feedback from the Editors below my signature.
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Thank you for submitting your manuscript to Royal Society Open Science and we look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Reviewer comments to Author: Reviewer: 1 Comments to the Author(s) The submitted paper was well written and some interesting results concerning the COVID-19 control have been provided, I do suggest that this paper could be accepted for publication RSOS.
Reviewer: 2 Comments to the Author(s) Comment on Manucript_RSOS-210823 In this manuscript, the authors developed an ODEs system consisting of two groups (HCW and members of the community) and investigated the optimal allocation of potentially scarce medical resources between these two groups to control the pandemic. The manuscript overall is wellwritten, and the methods and findings are illustrated with clear details. However, some concerns can be addressed to increase clarification: 1. My main concern is about the model setting. .013) that the three main causes for HCW infections are due to 1. HCW-to-HCW contacts; 2 HCW-to-Patient contacts; 3, environmental contamination. For the specialty of COVID-19, I am ok to consider HCW-tofriends/family/neighbors/other members of the community contact. But please clarify why you ignore patients (as another important group) if you try to control the infections for HCWs, since in my view if you ignore patients, you will greatly decrease the risk of HCWs. Is it a better idea to consider HCWs, patients, and other communities? Please clarify.
2. The authors used both the reproduction number and final size as measurements for control of the disease for different allocation strategies. As we know, the population of HCWs is relatively small compared to the general community). The final size F=F1+F2=Z1/N (the fraction of HCWs) +Z2/N(the fraction of community) is not fair to use since even though all HCWs are infected, F value can't be reflected dramatically. I would suggest using both F1 and F2 respectively to indicate the control of the disease since it is a big deal if the hospital's system is ruined by pandemics (e.g., most HCWs get infections). So it goes back to my #1 concern, please clarify the model set.
3. For table 1, it is best to have another column to indicate the source/reference of your parameter values even though in the text you mentioned some reference there. You should provide two versions of this manuscript and both versions must be provided in an editable format: one version should clearly identify all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting.
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See Appendix A.
Decision letter (RSOS-210823.R1) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.
Dear Dr Feng, I am pleased to inform you that your manuscript entitled "Optimal allocation of resources to health care workers or the general populace: a modeling study" is now accepted for publication in Royal Society Open Science.
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