Dynamic Estimation of Epidemiological Parameters of COVID-19 Outbreak and Effects of Interventions on Its Spread

Hongzhe Zhang; Xiaohang Zhao; Kexin Yin; Yiren Yan; Wei Qian; Bintong Chen; Xiao Fang

We assume that the diffusion of COVID-19 in Wuhan follows an epidemic model whose underlying time-dependent state variables Y t = (S t , I t , Q t , R t ) are from a dynamic system with system parameters Θ H = (β, µ, γ). These state variables and system parameters are summarized in Table 1 ; their meanings and the epidemic model will be elaborated in the next subsection. In particular, Q t represents the number of actively infected and quarantined cases by day t and R t represents the cumulative number of removed cases by day t. Ideally, we can obtain data about actual diffusion of COVID-19 over time. That is, ideally, we can have stochastically realized true values of Q t and R t for t = 1, 2, 3, · · · , denoted as Q e t and R e t . In general, if the realized true values of all state variables were known, we could estimate system parameters Θ H using well-developed statistical methods (e.g., 25, 26, 27 from frequentist perspectives). In reality, we only observe a subset of state variables with their officially reported numbers Q o t and R o t . Due to the under-reporting problem, these official numbers, Q o t and R o t , could be much lower than Q e t and R e t , respectively. As a result, directly applying an existing method to Q o t and R o t may not generate or reliably uncover the epidemiological parameters of COVID-19. To address this issue, we propose transformation functions that aim to recover Q e t and R e t from observed Q o t and R o t with some (unknown) transformation parameters Θ f .