Computation of Expected Epidemic Duration

This paper discusses the mean duration of a closed epidemic modeled by a discrete-time Markov chain. We develop a methodology for the efficient computation of the quantity of interest. The Markov chain model in consideration is bivariate, and is formally handled. We derive explicit terms for the probability to transition from one state to another, and prove that the chain is absorbing. The computation of the mean duration is translated to the computation of the expected hitting times to the set of absorbing states. We use the theory of absorbing Markov chains to derive a matrix formulation that gives way to an efficient algorithm to solve for the expected hitting times. This approach is instantiated in the form of a concrete algorithm, which is further optimized by using dynamic programming. Finally, we have implemented the method and tested it against the use of simulations to estimate mean durations. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement Financial support for this work was provided by the Flemish inter-university (iBOF) ''DESCARTES'' project. ### 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I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the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 are available online at