Estimating the within-household infection rate in emerging SIR epidemics among a community of households
This paper proposes a new method for estimating the within-household infection rate \(\lambda _L\) for an emerging (still in the exponential growing phase) SIR epidemic in a population of households. For this epidemic, it is assumed that an infective individual makes two types of contacts, namely local contacts, with random individuals from the household, and global contacts, with random individuals from the entire population. It is also assumed that the household size distribution and the exponential growth rate \(r\) are known and household-level data is available for a sample of households. The usual approach, the so-called basic MPLE method, which relies on fitting the final-size distribution for a single household based on the maximization of a certain pseudolikelihood function, is shown to be inadequate, as it leads to an underestimated \(\lambda _L\). An improved estimation is then obtained considering the impact of single-household epidemics which are still ongoing and using right-censoring (their size is assumed to be at least their current size), which leads to the so-called censored MPLE method. However, this estimation leads to an overestimated \(\lambda _L\). The authors then adapt the basic MPLE method by employing the asymptotic properties of supercritical branching processes and suitably redefining the pseudolikelihood function to be maximized. Under suitable assumptions, the resulting estimation is shown to be unbiased as the population and sample of households both tend to infinity. The theoretical framework is then illustrated for the Reed-Frost model using parameter choices based on data regarding the impact of varicella in UK. For this model, estimations of \(\lambda _L\) are given in terms of the secondary attack rate, defined as the probability that an infective infects locally a given household member, expressed as a percentage. It is observed that the new method is computationally feasible under the assumption of no latent period and exponentially distributed infectious period; possible extensions to age-structured populations or to diseases with a latent period are also outlined, along with a few caveats regarding the specifics of estimating \(r\) for an emerging epidemic.
scientific article; zbMATH DE number 6512485
scientific article