Prediction of the COVID-19 outbreak in China based on a new stochastic dynamic model

The rapid and widespread global spread of COVID-19 necessitates a strong understanding of its transmission dynamics to effectively manage and prevent its spread. Existing dynamic models, such as the Susceptible-Infected-Removed (SIR) model and its variants, have limitations when applied to COVID-19 due to the disease's unique characteristics. These characteristics include a significant asymptomatic population, the infectious nature of the disease during the incubation period, and the implementation of various intervention measures (traffic restrictions, contact tracing, mandatory mask use, screening, isolation, quarantine, and awareness campaigns). This study aims to address these limitations by developing a novel stochastic dynamic model that can accurately capture the COVID-19 outbreak's unique features and the impact of implemented control measures in mainland China. The model will be used to estimate key epidemiological parameters, predict epidemic development, estimate the number of unobservable carriers, determine epidemic containment dates, and assess the effectiveness of various control measures. The study focuses on several major provinces and cities in China, excluding Hubei province due to its unique challenges and distinct characteristics, reserving its analysis for future studies.

Existing studies employing deterministic compartmental models or extended SEIR models often neglect crucial aspects of COVID-19 transmission. For instance, some models assume non-infectiousness during the incubation period, which is contrary to evidence. Others ignore the impact of control measures like contact tracing and quarantine, or the delay between symptom onset and diagnosis. While some models incorporate the infectious incubation period, they may not accurately reflect the varying transmission probabilities between symptomatic and asymptomatic individuals. Although stochastic models have been used to study epidemics, their application to COVID-19 is relatively rare. Existing stochastic approaches often overlook the unique aspects of COVID-19, including the significant asymptomatic population, infectious incubation period, and implemented control measures. This study aims to improve upon the limitations of these existing models by developing a more comprehensive and realistic stochastic compartmental model.

The study utilized publicly available data on confirmed diagnoses, recoveries, and fatalities from six major provinces and cities in China (Beijing, Shanghai, Chongqing, Guangdong, Zhejiang, and Hunan). Population data were sourced from the China National Bureau of Statistics. Hubei province was excluded due to the overburdened medical resources, changing diagnostic criteria, and higher fatality rate. A novel stochastic compartmental model was developed with state variables representing susceptible (S), exposed (E), quarantined (Q), symptomatic infected (IN), hospitalized (IH), recovered (R), and dead (D) populations. The model accounts for the infectious incubation period, asymptomatic carriers, and implemented control measures. The model incorporates Poisson rates for various transitions between states, including infection, quarantine, hospitalization, symptom relief, recovery, and death. The transmission rate is assumed to vary over time, reflecting the impact of intervention measures. Parameter estimation used a state-collapsed version of the stochastic process to simplify the identification of initial values. Nine model parameters were estimated, some fixed based on existing studies (e.g., average time from symptom onset to diagnosis, mean incubation period). Others were estimated from the data using maximum likelihood estimation. The time-varying transmission rate was modeled as a piecewise constant function to reflect changes in intervention measures. Sensitivity analyses were conducted to assess the impact of variations in specific parameters, such as the recovery rate of asymptomatic individuals. Model predictions were generated through 1000 simulations to produce 95% confidence intervals for key population states, containment time, and the time-varying reproduction number (Rt). A hypothetical test with a zero quarantine probability (q = 0) was used to assess the effectiveness of the contact tracing policy.

The study's key findings include: (1) Approximately 30% of infections were asymptomatic, consistent with other studies; (2) Symptomatic individuals were approximately twice as likely to transmit the virus compared to asymptomatic individuals; (3) Containment measures effectively reduced transmission rates; (4) The model predicted the containment time of the outbreak in the studied regions to be between late February and early March; (5) The time-varying Rt was initially around 2, decreasing rapidly after the implementation of control measures; (6) The contact tracing policy significantly contributed to epidemic containment, as shown by a hypothetical test where the quarantine probability was set to zero, resulting in significant delays in containment time. The model accurately predicted the cumulative confirmed cases but slightly overestimated the number of hospitalized cases, possibly due to improvements in treatment shortening recovery time.

The proposed stochastic model offers a significant advancement in understanding COVID-19 transmission dynamics. Compared to previous models, it incorporates several key features—the infectious incubation period, the substantial asymptomatic population, and the implementation of contact tracing and quarantine measures with time latency. The model provides insights into the relative transmission probabilities of symptomatic and asymptomatic individuals, and demonstrates the effectiveness of intervention strategies in curtailing the spread. The model's predictions align with observed data, reinforcing its validity and usefulness in forecasting epidemic trends and assessing the impact of control measures. The findings highlight the importance of comprehensive testing, contact tracing, and quarantine in controlling outbreaks, providing crucial insights for public health strategies. The limitations of the model, such as potential identification issues for some parameters and the reliance on data collected before February 22nd, are noted and potential future research directions are suggested.

This study presents a novel stochastic model that effectively captures the unique characteristics of the COVID-19 outbreak in China and the effect of intervention strategies. The model's predictions and findings demonstrate the significance of asymptomatic transmission and the effectiveness of control measures. While limitations exist, the model offers valuable insights for public health response and future research directions include incorporating more realistic medical tracking dynamics, medical service capacity, and population flows between cities to improve the model's accuracy and generalizability.

The model has several limitations. First, due to limited data, there is a risk of parameter identification issues, particularly for parameters less directly related to observable states. Second, the model's applicability is limited if significant changes occur in the epidemic control or treatment measures. Third, the model might require modifications if a non-negligible proportion of asymptomatic patients remain infectious after quarantine. Finally, parameter estimation precision might be affected if the simplified model differs significantly from the more complex reality.