I am currently studying the model described in this study for estimating the COVID19 deaths. Their model is a Bayesian, and is fairly simple. Let $Y_1, Y_2, \ldots Y_n$ be the number of deaths on day $1, 2, 3, \ldots, n$. The model for $Y_i$ is then \begin{align} Y_i &\sim \text{Poisson}(\lambda_i) \\ \log(\lambda_i) &= \log(p) + \log(SK(i \mid \alpha, \beta, \nu)) + \log(K) \end{align}
where $SK$ is a Skew Normal distribution, $K$ is the population size, and $p$ is the maximum asymptotic level parameter. I am not really sure what this term is doing nor why it's necessary in the model. Is it so that $\lambda$ dosn't blow up to infinity? I thought that whats the $K$ (i.e. population size) was suppose to do.
