Computation of Expected Epidemic Duration
Alarcon Gonzalez, A.; Perez, G. A.; Rao, S.
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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.
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