Copula-based CUSUM charts for monitoring infectious disease using Markovian Poisson processes

The manuscript addresses the copula-based CUSUM charting scheme to monitor infectious disease. To facilitate the disease surveillance, the Poisson distribution is often used to model the number of diseases counts while the Markov process is used to model the serial correlation within sequential observations. In literature, the first-order autoregressive (AR(1)) process and the first-order integer autoregressive (INAR(1)) process have been used to model continuous observations and Poisson-distributed counts respectively when there exists the Markovian structure between two adjacent observations. However, both of them only describe the conditional linear correlation between adjacent observations. In this paper, the copula model is employed to fit board ranges of correlation structures in the Markovian Poisson processes especially when the conditional correlation between two adjacent Poisson observations is nonlinear. Further, a CUSUM chart based on the log-likelihood ratio is developed to monitor the Poisson processes. The proposed chart performs better in detecting Poisson counts when comparing with existing control charts, and the proposed CUSUM chart performs even better under moderate and strong dependence. A real case study of the counts COVID-19 cases in China is adopted to investigated the effectiveness of our proposed chart. Therefore, it supplies a new method for monitoring the potential changes of the disease infection.