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

COVID-19 spread rapidly worldwide and prompted extensive control measures in Mainland China beginning January 19, 2020, including a lockdown of Wuhan on January 23, 2020. Effective control and prevention require understanding the epidemic dynamics. Classic compartmental models (e.g., SIR/SEIR and their modifications) have been widely used but often fail to capture key features of COVID-19 such as infectious incubation, asymptomatic transmission, and delays in contact tracing and quarantine. This study proposes a novel stochastic compartmental model designed to reflect these unique aspects, estimate key epidemiological parameters, predict epidemic trajectories, infer unobservable carriers and containment dates, and assess the impact of interventions in major provinces and cities in China outside Hubei.

Deterministic ODE/DE models have been extensively applied to SARS, H1N1, and COVID-19. Tang et al. proposed a model incorporating clinical and intervention factors but assumed non-infectious incubation and immediate quarantine after infection, which do not hold for COVID-19. Wu et al. developed an extended SEIR with inter-city transmission but omitted control measures and assumed no pre-symptomatic infectiousness. Yang et al. used a discrete-time model allowing infectious incubation but assumed identical transmission probabilities for symptomatic and asymptomatic carriers, which is questionable. While deterministic models can be seen as mean-field limits of stochastic models, randomness is non-negligible when outbreak size is small relative to the population, making stochastic models preferable for uncertainty quantification and for incorporating individual variation and spatial structure. Early COVID-19 stochastic approaches were limited (e.g., exponential growth fits), and Chinazzi et al. used a discrete-time stochastic model for travel restriction effects but did not fully capture infectious incubation, asymptomatic carriers, and realistic contact tracing. These gaps motivate a stochastic model tailored to COVID-19’s unique transmission and intervention dynamics.

Data: Daily numbers of confirmed diagnoses, recoveries, and fatalities were collected for Beijing, Shanghai, Chongqing, Guangdong, Zhejiang, and Hunan from local Health Commissions; population sizes were obtained from the National Bureau of Statistics. Hubei was excluded due to overwhelmed medical resources, changes in diagnostic criteria in mid-February, and substantially higher fatality rates, which would require a different model. Model: A continuous-time Markov stochastic compartmental model with states S (susceptible), E (exposed/infectious incubation including asymptomatic), Q (quarantined), IN (infectious symptomatic, not yet hospitalized), IH (hospitalized), R (recovered), and D (dead). Transitions: (i) Infection by E or IN at Poisson rates λ_E = θ λ_IN and λ_IN, respectively; with probability p an infection becomes symptomatic (future IN) at rate r_s (incubation), otherwise asymptomatic; contacts are traceable with probability q. (ii) Traceable secondary cases are quarantined at rate r_1 (losing infectivity) and remain isolated/hospitalized to outcome. (iii) Symptomatic IN are hospitalized (IH) at rate r_H; with probabilities p and 1−p classified as light/mild vs severe. (iv) Severe inpatients may relieve to mild at rate r_s. (v) Recoveries occur from asymptomatic (γ_A), symptomatic but not hospitalized (γ_IN), and hospitalized mild (γ_IH). (vi) Deaths occur from IN (δ_IN) and hospitalized severe (δ_H). A state-collapsed version is used for parameter inference to ease identifiability. Parameter estimation: Observed time series include IH(t) (standing confirmed hospitalized) and a substate of R (reported recoveries). Latent states include S, E, Q, IN, and unobserved parts of R. Initial conditions: S(0) approximated by regional population; quarantine absent pre–Jan 23 so E_q(0)=0; R(0) set arbitrarily without affecting inference; IN(0) and E(0) treated as unknowns and estimated. Parameters per region: λ_IN, θ, p, q, γ_IN, γ_A, γ_IH, r_1, r_H (with r_1, r_s, r_H informed by literature: r_1 is inverse of mean time from symptom onset to diagnosis; r_s inverse mean incubation; r_H inverse of mean difference between infectious period and serial interval). γ_A weakly informed by data and set to 1/10 with sensitivity analysis. Parameters p and death rates δ assumed common across regions; λ_IN, q, γ_IH allowed to vary by region and to be time-varying to reflect interventions. Piecewise-constant time-variation: λ_IN(t)=λ_IN for t<T1 and λ′_IN for t≥T1 with T1=Jan 29 (based on observed rate changes); γ_IH(t)=γ_IH for t<T2 and γ′_IH for t≥T2, where T2 is chosen per region from observed ΔR_IH(t). Likelihood-based estimation using the collapsed stochastic process; details in Supplementary C. Prediction and evaluation: Using estimated parameters, 1000 stochastic simulations per region generate trajectories and 95% confidence intervals for key quantities: accumulated confirmed (IH+R+D), current hospitalized (IH), and active carriers (E+IN). Containment time is defined as the first day active carriers fall below threshold T=10. Time-varying controlled reproduction number R_t is approximated from the model (Supplementary D). A counterfactual assesses medical tracking effectiveness by setting q=0 while holding other parameters fixed. Model was fitted to data up to Feb 22, 2020; later data used for evaluation.

• Approximately 30% of infections are asymptomatic; estimates of p were robust to γ_A choices. • Symptomatic carriers are about twice as likely to transmit as asymptomatic carriers (higher λ_IN relative to θλ_IN). • Quarantine traceability probability q is highest in Zhejiang, consistent with extensive contact tracing (over 40,000 contacts traced by Mar 2, 2020); q increases slightly as assumed γ_A decreases. • Initial latent populations E(0) and IN(0) vary with γ_A choice but remain within the same order of magnitude across regions. • Contact/transmission rate λ_IN decreased markedly after interventions around Jan 29; γ_IH improved over time in some regions. • Model predictions (using data through Feb 22) captured accumulated confirmed counts within 95% intervals; IH tended to be overestimated likely due to shortened recovery time later. • Predicted containment (active carriers below 10) occurred between late February and mid-March: earliest in Shanghai (~Feb 28) and latest in Guangdong (~Mar 15); predictions were consistent for Beijing, Shanghai, Guangdong and slightly overestimated for Chongqing, Hunan, Zhejiang. • Estimated R_t was typically between 2 and 3 before interventions, dropping rapidly to about 0.2 between Jan 29 and Feb 1 across regions. • Counterfactual with q=0 still contained the epidemic due to reduced contacts and diagnosis delays, but significantly delayed containment dates, indicating a substantial contribution of contact tracing to control.

The stochastic model incorporating infectious incubation, asymptomatic transmission, and delayed contact tracing successfully explains observed dynamics in six major Chinese regions and quantifies intervention impacts. It estimates a substantial asymptomatic fraction (~30%), higher transmissibility for symptomatic cases (approximately double), and a sharp reduction in transmission following control measures, with R_t falling well below 1 shortly after Jan 29. Predicted containment windows align with observed trends, supporting the model’s utility for real-time planning. The analysis underscores the importance of combined measures: reducing contact rates, expedited diagnosis/hospitalization, and effective contact tracing/quarantine. Policy recommendations include enabling testing without symptoms, implementing and maintaining robust contact tracing with quarantine, and sustaining exposure-reduction measures. The model also indicates considerable resurgence risk if measures are relaxed too soon: estimated probabilities of resurgence in Beijing are 0.415 if relaxed three weeks after containment, 0.658 after two weeks, and 0.878 after one week, highlighting the need for cautious de-escalation. Results are broadly consistent with prior estimates of R_t and transmission characteristics, reinforcing their relevance to epidemic control strategies.

This study introduces a novel stochastic compartmental model that captures key COVID-19 features—infectious incubation, asymptomatic carriers, and realistic contact tracing delays—and links them to intervention effects. It provides parameter estimates, forecasts, and assessments of control policies for several Chinese regions, accurately reflecting epidemic trajectories and containment timing. Future research will extend the framework to: (i) more realistic, diagnosis-triggered medical tracking dynamics using individual-based modeling; (ii) explicit modeling of medical service capacity constraints; and (iii) incorporation of inter-regional population flows and travel-related transmission with behaviorally responsive mobility.

• Potential identifiability issues for parameters weakly connected to observed data, especially in the collapsed model. • Model applicability may diminish if control or treatment strategies change substantially. • The framework may require modification if a significant fraction of asymptomatic individuals remains infectious after quarantine. • Parameter estimates may lose precision if discrepancies between the full stochastic process and its simplified version are large.