@article {1454,
	title = {An exact and implementable computation of the final outbreak size distribution under Erlang distributed infectious period},
	journal = {Mathematical Biosciences},
	volume = {325},
	year = {2020},
	pages = {108363},
	abstract = {<p>This paper deals with a stochastic SIR (Susceptible{\textendash}Infected{\textendash}Recovered) model with Erlang(k,μ) distributed infectious period commonly referred as SIkR model. We show that using the total number of remaining Erlang stages as the state variable, we do not need to keep track of the stages of individual infections, and can employ a first step analysis to efficiently obtain quantities of interest. We study the distribution of the total number of recovered individuals and the distribution of the maximum number of individuals who are simultaneously infected until the end of the disease. In the literature, final outbreak size is calculated only for a small population size exactly and derivations of approximate analytic solutions from asymptotic results are suggested for larger population sizes. We numerically demonstrate that our methods are implementable on large size problem instances.</p>},
	keywords = {Erlang distributed infectious period, Final size distribution, Markov models, Maximum size distribution, Stochastic SIR},
	issn = {0025-5564},
	doi = {https://doi.org/10.1016/j.mbs.2020.108363},
	url = {https://www.sciencedirect.com/science/article/pii/S0025556420300547},
	author = {Zeynep G{\"o}k{\c c}e {\.I}{\c s}lier and Refik G{\"u}ll{\"u} and Wolfgang H{\"o}rmann}
}
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	title = {Efficient simulations for a Bernoulli mixture model of portfolio credit risk},
	journal = {Annals of Operations Research},
	volume = {260},
	year = {2018},
	pages = {113{\textendash}128},
	author = {Ba{\c s}o{\u g}lu, {\.I}smail and Wolfgang H{\"o}rmann and Sak, Halis}
}
@conference {Derflinger;Hoermann;Leydold;Sak:2009a,
	title = {Efficient Numerical Inversion for Financial Simulations},
	booktitle = {Monte Carlo and Quasi-Monte Carlo Methods 2008},
	year = {2009},
	pages = {297{\textendash}304},
	publisher = {Springer-Verlag},
	organization = {Springer-Verlag},
	address = {Heidelberg},
	author = {Derflinger, Gerhard and Wolfgang H{\"o}rmann and Leydold, Josef and Sak, Halis}
}
@article {Tirler;etal:2004a,
	title = {An Error in the {Kinderman-Ramage} Method and How to Fix It},
	journal = {Computational Statistics and Data Analysis},
	volume = {47},
	number = {3},
	year = {2004},
	pages = {433{\textendash}440},
	author = {Tirler, G{\"u}nter and Dalgaard, Peter and Wolfgang H{\"o}rmann and Leydold, Josef}
}
