Stochastic modelling of the effects of human-mobility restriction and viral infection characteristics on the spread of COVID-19
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Abstract
After several months of "lockdown" as the sole answer to the COVID-19 pandemic, balancing the re-opening of society against the implementation of non-pharmaceutical measures needed for minimizing interpersonal contacts has become important. Here, we present a stochastic model that examines this problem. In our model, people are allowed to move between discrete positions on a one-dimensional grid with viral infection possible when two people are collocated at the same site. Our model features three sets of adjustable parameters, which characterize (i) viral transmission, (ii) viral detection, and (iii) degree of personal mobility, and as such, it is able to provide a qualitative assessment of the potential for second-wave infection outbreaks based on the timing, extent, and pattern of the lockdown relaxation strategies. Our results suggest that a full lockdown will yield the lowest number of infections (as anticipated) but we also found that when personal mobility exceeded a critical level, infections increased, quickly reaching a plateau that depended solely on the population density. Confinement was not effective if not accompanied by a detection/quarantine capacity surpassing 40% of the symptomatic patients. Finally, taking action to ensure a viral transmission probability of less than 0.4, which, in real life, may mean actions such as social distancing or mask-wearing, could be as effective as a soft lockdown.
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SciScore for 10.1101/2020.07.28.20163980: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
Software and Algorithms Sentences Resources vii) Simulation Particulars: The programs were encoded using python (3.4.8), and random numbers were generated using the python "rand" function. pythonsuggested: (IPython, RRID:SCR_001658)Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:
Nevertheless, …
SciScore for 10.1101/2020.07.28.20163980: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
Software and Algorithms Sentences Resources vii) Simulation Particulars: The programs were encoded using python (3.4.8), and random numbers were generated using the python "rand" function. pythonsuggested: (IPython, RRID:SCR_001658)Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:
Nevertheless, despite these limitations, we believe that our model provides useful qualitative and semi-quantitative information on how virus-specific and society specific parameters influence the way viral spread occurs during periods of lockdown and re-opening. While some observations were anticipated, such as an early lockdown being more effective than a delayed one, others were less intuitive. For example, the relationship between mobility and the probability of encounters were indeed critically dependent upon both the initial distribution of the population and the population density. Furthermore, our model predicts that the mobility restriction must be stringently enforced and accompanied by a high detection/isolation probability in order to reduce the total number of infections significantly. Finally, the detection and quarantine of presymptomatic patients (which would require testing a large number of people every day and is therefore not a realistic strategy) would reduce the final number of infections by a factor of ten or more. Successful strategies for achieving a low number of infections include full confinement combined with a reasonable detection probability of symptomatic patients (DP > 0.4). A realistic strategy might be mild confinement, with a high detection probability during the symptomatic phase and a reasonable detection probability during the pre-symptomatic phase (for example, m =5, DP =0.8, DP2 = 20 in Table 1c. Such strategy is in line with a recent report by Muller et al.[22]). Variation in such factors may be the reason behind the wide variation of infection numbers observed in different countries [23]. Conclusion We presented a stochastic coarse grained model where people were allowed to either move freely or in a constrained manner, and viral transmission can occur when infected and non-infected individuals overlap at the same site. Our model includes adjustable parameters characterizing viral transmission probability, detection probability, and personal mobility within a population. Importantly, our simulation can reproduce the basic aspects of viral spread within a community and the development of a local epidemic. The results of our simulation agreed well with exact probabilistic calculations, which, under certain simple limiting cases, were readily formulated. Although many of the results were in line with our anticipation, our model revealed a number of interesting features. In particular, we noticed that the link between personal mobility and the risk of encounter (and thus infection) is a step function when the initial distribution is regularly-spaced, and the maximum mobility lies below the inverse spatial density of the population. Below this critical juncture, the risks of infection were zero, whereas at greater mobility (or higher population density) the situation rapidly approached the random case. The approach described here provides a qualitative assessment of the efficacy of modifying societal parameters that should prove useful to decision-makers when considering the relaxation of lockdown conditions. Acknowledgments: This research was motivated by an intense discussion with Prof. Christopher Mudry (Paul Scherrer Institute and Ecole Polytechnique de Lausanne, Switzerland), for which Y.K. is very thankful. We thank Ms. Jingwen Xian and Mr. Zhirui Cheng for discussion and Python programming of the early versions. D.H. would like to thank the Nagoya Institute of Technology for a placement on their Visiting International Scientist Program. Funding: This research was supported by a JSPS grant-in-aid for scientific research (KAKENHI, 15H04359, and 18H02385) Competing interests: The authors declare no competing interests. Data Sharing: All data are given in the manuscript and the supplementary data. The original program can be freely accessed at http://domserv.lab.tuat.ac.jp/covid19.html (under preparation) Authors Contribution: Y.K., and Y.M. designed the project, Y.K., Y.M., and D.H. derived the equations described in the appendix, Y.K., and D.H. wrote the manuscript, H.T. and T.M. discussed the results and advised with paper writing, Y.M. and S.A. wrote the program performed simulation. All authors read and approved the manuscript. Footnote1: We are aware of a number of reports describing the potential for COVID-19 reinfection of previously recovered patients [[24-26]]. Although this situation is considered uncommon, the simulation could be readily modified to include such a scenario.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
About SciScore
SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information scattered throughout a paper in a standard, easy to digest format. SciScore is not a substitute for expert review. SciScore checks for the presence and correctness of RRIDs (research resource identifiers) in the manuscript, and detects sentences that appear to be missing RRIDs. SciScore also checks to make sure that rigor criteria are addressed by authors. It does this by detecting sentences that discuss criteria such as blinding or power analysis. SciScore does not guarantee that the rigor criteria that it detects are appropriate for the particular study. Instead it assists authors, editors, and reviewers by drawing attention to sections of the manuscript that contain or should contain various rigor criteria and key resources. For details on the results shown here, including references cited, please follow this link.
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SciScore for 10.1101/2020.07.28.20163980: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:Nevertheless, despite these limitations, we believe that our model provides useful qualitative and semi-quantitative information on how virus-specific and society specific parameters influence the way viral spread occurs during periods of lockdown and re-opening. While some observations were anticipated, such as an early lockdown being …
SciScore for 10.1101/2020.07.28.20163980: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:Nevertheless, despite these limitations, we believe that our model provides useful qualitative and semi-quantitative information on how virus-specific and society specific parameters influence the way viral spread occurs during periods of lockdown and re-opening. While some observations were anticipated, such as an early lockdown being more effective than a delayed one, others were less intuitive. For example, the relationship between mobility and the probability of encounters were indeed critically dependent upon both the initial distribution of the population and the population density. Furthermore, our model predicts that the mobility restriction must be stringently enforced and accompanied by a high detection/isolation probability in order to reduce the total number of infections significantly. Finally, the detection and quarantine of pre-symptomatic patients (which would require testing a large number of people every day and is therefore not a realistic strategy) would reduce the final number of infections by a factor of ten or more. Successful strategies for achieving a low number of infections include full confinement combined with a reasonable detection probability of symptomatic patients (DP > 0.4). A realistic strategy might be mild confinement, with a high detection probability during the symptomatic phase and a reasonable detection probability during the pre-symptomatic phase (for example, m =5, DP =0.8, DP2 = 20 in Table 1c. Such strategy is in line with a recent...
Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
Results from rtransparent:- Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
- Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
- No protocol registration statement was detected.
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SciScore for 10.1101/2020.07.28.20163980: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
Software and Algorithms Sentences Resources Jingwen Xian and Mr. Zhirui Cheng for discussion and Python programming of the early versions. Pythonsuggested: (IPython, SCR_001658)Data from additional tools added to each annotation on a weekly basis.
About SciScore
SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information scattered throughout a paper in a standard, easy to digest format. SciScore is not a substitute for expert review. SciScore checks for the presence and correctness of RRIDs …
SciScore for 10.1101/2020.07.28.20163980: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
Software and Algorithms Sentences Resources Jingwen Xian and Mr. Zhirui Cheng for discussion and Python programming of the early versions. Pythonsuggested: (IPython, SCR_001658)Data from additional tools added to each annotation on a weekly basis.
About SciScore
SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information scattered throughout a paper in a standard, easy to digest format. SciScore is not a substitute for expert review. SciScore checks for the presence and correctness of RRIDs (research resource identifiers) in the manuscript, and detects sentences that appear to be missing RRIDs. SciScore also checks to make sure that rigor criteria are addressed by authors. It does this by detecting sentences that discuss criteria such as blinding or power analysis. SciScore does not guarantee that the rigor criteria that it detects are appropriate for the particular study. Instead it assists authors, editors, and reviewers by drawing attention to sections of the manuscript that contain or should contain various rigor criteria and key resources. For details on the results shown here, including references cited, please follow this link.
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