Approximate relationships between SIR and logistic models

Infectious epidemics are often described using a three-compartment Susceptible-Infectious-Removed (SIR) model, whose solution can be shown to involve generalizations of the logistic distribution. Using mathematical relationships relating these generalized logistic distributions, the population proportion remaining Susceptible can be approximated using the inverse of a standard cumulative logistic distribution, while the population proportion actively Infectious can be approximated using the density of a logistic or log-logistic distribution. Conversely, the parameters of an underlying SIR model can be approximately inferred from population-based data that have been estimated using logistic and/or log-logistic models. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement No third party funding. All authors employed by Maine Medical Center or MaineHealth. ### 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below: N/A All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived. 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 N/A