Scaling rules for pandemics: Estimating infected fraction from identified cases for the SARS-Cov-2 Pandemic

Using a modified form of the SIR model, we show that, under general conditions, all pandemics exhibit certain scaling rules. Using only daily data for symptomatic, confirmed cases, these scaling rules can be used to estimate: (i) reff, the effective pandemic R-parameter; (ii) ftot, the fraction of exposed individuals that were infected (symptomatic and asymptomatic); (iii) Leff, the effective latency, the average number of days an infected individual is able to infect others in the pool of susceptible individuals; and (iv) α, the probability of infection per contact between infected and susceptible individuals. We validate the scaling rules using an example and then apply our method to estimate reff, ftot, Leff and α for the first phase of the SARS-Cov-2, Covid-19 pandemic for several countries where there was a well separated first peak in identified infected daily cases after the outbreak of the pandemic in early 2020. Our results are general and can be applied to any pandemic. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement GB was partly supported by grants from DoD (KC180159) and NIH (P01CA250957). GB thanks Professor Charles DeLisi for many discussions and collaboration on earlier (unpublished) work on the SARS-CoV-2 pandemic using the SIR model. GB and SD thank the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611, and the Geballe Lab for Advanced Materials at Stanford University for their hospitality while this work was done. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: This study only used publicly available data on SARS-CoV-2 cases and deaths from the World Health Organization Website: I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes The data and Matlab codes used in this paper are available on request to gyanbhanot{at}gmail.com. The data used to fit the model to actual pandemic data is in Supplementary Table 1. The World Health Organization country specific data we used for the SARS-CoV-2 pandemic is in Supplementary Table 2. The data in Supplementary Figures and Tables is available online at: