Stochastic epidemic models and their link with methods from survival analysis

Compartmental models based on ordinary differential equations (ODE’s) quantifying the interactions between susceptible, infectious, and recovered individuals within a population have played an important role in infectious disease modeling. The aim of the present paper is to explain the link between stochastic epidemic models based on the susceptible-infectious-recovered (SIR) model, and methods from survival analysis. We illustrate how standard software for survival analysis in the statistical language R can be used to estimate pivotal parameters in the stochastic SIR model in the very much idealized situation where the epidemic is completely observed. Extensions incorporating interventions, age structure and heterogeneity are explored and illustrated. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study did not receive any funding ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the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, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced in the present study are available upon reasonable request to the authors