Reproduction numbers for epidemic models with households and other social structures. I. Definition and calculation of R0

Pellis, Lorenzo; Ball, Frank; Trapman, Pieter

doi:10.1016/j.mbs.2011.10.009

Cited by 73 publications

(118 citation statements)

References 41 publications

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“…and for (a, b) = (h − 1, 1), For n ≥ 1, we assume the inductive hypothesis that for 0 ≤ k ≤ n − 1, y (k) (h−1,1) = x k,0 . Then from (3.24), we have that Therefore we have shown that the two representations of the household epidemic given in [14] and in this paper give the same mean number of infectives and the same mean number of new household epidemics in generation n (n = 0, 1, . .…”

Section: Sir Household Epidemic Modelmentioning

confidence: 59%

“…is straightforward using [14], Appendix A and we provide a brief outline in Appendix A how similar arguments to those used in Section 3.1 can be used to show that R r 0 is the maximal eigenvalue of M R .…”

Section: Discussionmentioning

confidence: 99%

“…. , h − 1) be defined as in [14], Lemma 1, with x n,i denoting the mean number of individuals in the n th generation of the epidemic who belong to the i th generation of the household epidemic. We again employ the convention that the initial infective individual in the household represents generation 0.…”

Section: Sir Household Epidemic Modelmentioning

confidence: 99%

“…We begin by computing the transition probabilities for a household epidemic in state (a, b), a susceptibles and b infectives. By considering the total amount of infection, I b , generated by the b infectives and the fact that the infectious periods, T , are independent and identically distributed, it was shown in [14], We can proceed along identical lines to (3.7) in decomposing M R into…”

Section: A Construction Of M Rmentioning

confidence: 99%

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The basic reproduction number, R0, in structured populations

Neal

Theparod

2019

Mathematical Biosciences

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In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, R0, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both SIR and SIS epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household model, we show that our expression for R0 agrees with earlier work despite the alternative nature of the construction of the mean reproductive matrix, and hence, the basic reproduction number.

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Section: Sir Household Epidemic Modelmentioning

confidence: 59%

Section: Discussionmentioning

confidence: 99%

Section: Sir Household Epidemic Modelmentioning

confidence: 99%

Section: A Construction Of M Rmentioning

confidence: 99%

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The basic reproduction number, R0, in structured populations

Neal

Theparod

2019

Mathematical Biosciences

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“…Unlike more traditional pandemic analyses, the basic reproductive number, R 0 , is not used as a measure of pandemic severity. The basic reproductive number, R 0 , is defined to be the expected number of secondary infections caused by one infected individual in an otherwise fully susceptible population (Anderson and May 1991;Pellis et al 2012). In a population with household structure, the basic reproductive number cannot reliably be used to predict the severity of an outbreak (Ball et al 1997;Ross et al 2010).…”

Section: Parametersmentioning

confidence: 99%

Choice of Antiviral Allocation Scheme for Pandemic Influenza Depends on Strain Transmissibility, Delivery Delay and Stockpile Size

et al. 2016

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Recently, pandemic response has involved the use of antivirals. These antivirals are often allocated to households dynamically throughout the pandemic with the aim being to retard the spread of infection. A drawback of this is that there is a delay until infection is confirmed and antivirals are delivered. Here an alternative allocation scheme is considered, where antivirals are instead preallocated to households at the start of a pandemic, thus reducing this delay. To compare these two schemes, a deterministic approximation to a novel stochastic household model is derived, which allows efficient computation of key quantities such as the expected epidemic final size, expected early growth rate, expected peak size and expected peak time of the epidemic. It is found that the theoretical best choice of allocation scheme depends on strain transmissibility, the delay in delivering antivirals under a dynamic allocation scheme and the stockpile size. A broad summary is that for realistic stockpile sizes, a dynamic allocation scheme is superior with the important exception of the epidemic final size under a severe pandemic scenario. Our results, viewed in conjunction with the practical considerations of implementing a preallocation scheme, support a focus on attempting to reduce the delay in delivering antivirals under a dynamic allocation scheme during a future pandemic.

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