Time series analysis of cumulative incidences of typhoid and paratyphoid fevers in China using both Grey and SARIMA models

Typhoid and paratyphoid fevers are common enteric diseases causing disability and death in China. Incidence data of typhoid and paratyphoid between 2004 and 2016 in China were analyzed descriptively to explore the epidemiological features such as age-specific and geographical distribution. Cumulative incidence of both fevers displayed significant decrease nationally, displaying a drop of 73.9% for typhoid and 86.6% for paratyphoid in 2016 compared to 2004. Cumulative incidence fell in all age subgroups and the 0-4 years-old children were the most susceptible ones in recent years. A cluster of three southwestern provinces (Yunnan, Guizhou, and Guangxi) were the top high-incidence regions. Grey model GM (1,1) and seasonal autoregressive integrated moving average (SARIMA) model were employed to extract the long-term trends of the diseases. Annual cumulative incidence for typhoid and paratyphoid were formulated by GM (1,1) as (x) over cap (t)=-14.98(e(-0.10(t-2004)) - e(-0.10(t-2005))) and (x) over cap (t)=-4.96(e(-0.19(t-2004)) - e(-0.19(t-2005))) respectively. SARIMA (0,1,7) x (1,0,1)(12) was selected among a collection of constructed models for high R-2 and low errors. The predictive models for both fevers forecasted cumulative incidence to continue the slightly downward trend and maintain the cyclical seasonality in near future years. Such data-driven insights are informative and actionable for the prevention and control of typhoid and paratyphoid fevers as serious infectious diseases.