### Mathematical Biosciences and Engineering

2009, Issue 3: 509-520. doi: 10.3934/mbe.2009.6.509

# Applications of occupancy urn models to epidemiology

• Received: 01 February 2008 Accepted: 29 June 2018 Published: 01 June 2009
• MSC : Primary: 62P10; Secondary: 92B05.

• This paper shows how occupancy urn models can be used to derive useful results in epidemiology. First we show how simple epidemic models can be re-interpreted in terms of occupancy problems. We use this reformulation to derive an expression for the expected epidemic size, that is, the total number of infected at the end of an outbreak. We also use this approach to derive point and interval estimates of the Basic Reproduction Ratio, $R_{0}$. We show that this construction does not require that the underlying SIR model be a homogeneous Poisson process, leading to a geometric distribution for the number of contacts before removal, but instead it supports a general distribution. The urn model construction is easy to handle and represents a rich field for further exploitation.

Citation: Carlos M. Hernández-Suárez, Oliver Mendoza-Cano. Applications of occupancy urn models to epidemiology[J]. Mathematical Biosciences and Engineering, 2009, 6(3): 509-520. doi: 10.3934/mbe.2009.6.509

### Related Papers:

• This paper shows how occupancy urn models can be used to derive useful results in epidemiology. First we show how simple epidemic models can be re-interpreted in terms of occupancy problems. We use this reformulation to derive an expression for the expected epidemic size, that is, the total number of infected at the end of an outbreak. We also use this approach to derive point and interval estimates of the Basic Reproduction Ratio, $R_{0}$. We show that this construction does not require that the underlying SIR model be a homogeneous Poisson process, leading to a geometric distribution for the number of contacts before removal, but instead it supports a general distribution. The urn model construction is easy to handle and represents a rich field for further exploitation.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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