The COVID-19 pandemic exposed limitations of classical compartmental models that assume homogeneous transmission and constant contact rates. We have proposed U-SEIR, a unified six-compartment framework integrating an undetected/asymptomatic compartment, a super-spreader compartment, and a time-varying contact rate $ \beta(t) = \beta_{0}e^{-\mu t} $ representing cumulative non-pharmaceutical interventions. The basic reproduction number was derived via the next-generation matrix, and the disease-free equilibrium was proved globally asymptotically stable when $ \mathcal{R}_{0} < 1 $ by a Lyapunov argument. The model was validated on daily new-case series of five countries (China/Hubei, USA, UK, Japan, Italy) and one sub-national province (Hunan) during the first wave. A controlled comparison isolated the contributions of the intervention mechanism and structural complexity: for China/Hubei, the no-control susceptible-infectious-recovered (SIR) yielded $ R^{2} = -0.47 $, whereas the same model with the time-varying contact rate reached $ R^{2} = 0.98 $. A paired block bootstrap ($ B = 500 $, block = 7 days) and AIC (Akaike Information Criterion) showed that the asymptomatic and super-spreader compartments provide a statistically distinguishable improvement over the best $ \beta(t) $-controlled susceptible-exposed-infectious-recovered (SEIR) baseline in only one of six jurisdictions (Italy, $ p < 0.001 $, $ \Delta\mathrm{AIC} = 7.5 $). Identifiability analysis showed the eleven-parameter fit is borderline identifiable ($ \kappa_{\mathrm{FIM}} $ in the $ 10^{12} $–$ 10^{22} $ range, with $ \beta_0 $ and $ \mu $ jointly unidentifiable on a narrow ridge); fixing five parameters at clinical values and re-fitting a reduced $ K' = 6 $ model lowered the Fisher-information condition number by four to seven orders of magnitude, with profile-likelihood intervals, a structural-identifiability check, and Markov Chain Monte Carlo (MCMC) credible intervals propagated through all scenario analyses. The central finding was that intervention dynamics, not structural complexity, dominate fit quality in jurisdictions with strict lockdowns.
Citation: Shujiang Tang. A unified compartmental model (U-SEIR) integrating asymptomatic infection, super-spreading, and time-varying non-pharmaceutical interventions for the first wave of COVID-19[J]. Mathematical Biosciences and Engineering, 2026, 23(10): 3138-3168. doi: 10.3934/mbe.2026108
The COVID-19 pandemic exposed limitations of classical compartmental models that assume homogeneous transmission and constant contact rates. We have proposed U-SEIR, a unified six-compartment framework integrating an undetected/asymptomatic compartment, a super-spreader compartment, and a time-varying contact rate $ \beta(t) = \beta_{0}e^{-\mu t} $ representing cumulative non-pharmaceutical interventions. The basic reproduction number was derived via the next-generation matrix, and the disease-free equilibrium was proved globally asymptotically stable when $ \mathcal{R}_{0} < 1 $ by a Lyapunov argument. The model was validated on daily new-case series of five countries (China/Hubei, USA, UK, Japan, Italy) and one sub-national province (Hunan) during the first wave. A controlled comparison isolated the contributions of the intervention mechanism and structural complexity: for China/Hubei, the no-control susceptible-infectious-recovered (SIR) yielded $ R^{2} = -0.47 $, whereas the same model with the time-varying contact rate reached $ R^{2} = 0.98 $. A paired block bootstrap ($ B = 500 $, block = 7 days) and AIC (Akaike Information Criterion) showed that the asymptomatic and super-spreader compartments provide a statistically distinguishable improvement over the best $ \beta(t) $-controlled susceptible-exposed-infectious-recovered (SEIR) baseline in only one of six jurisdictions (Italy, $ p < 0.001 $, $ \Delta\mathrm{AIC} = 7.5 $). Identifiability analysis showed the eleven-parameter fit is borderline identifiable ($ \kappa_{\mathrm{FIM}} $ in the $ 10^{12} $–$ 10^{22} $ range, with $ \beta_0 $ and $ \mu $ jointly unidentifiable on a narrow ridge); fixing five parameters at clinical values and re-fitting a reduced $ K' = 6 $ model lowered the Fisher-information condition number by four to seven orders of magnitude, with profile-likelihood intervals, a structural-identifiability check, and Markov Chain Monte Carlo (MCMC) credible intervals propagated through all scenario analyses. The central finding was that intervention dynamics, not structural complexity, dominate fit quality in jurisdictions with strict lockdowns.
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Shujiang Tang. A unified compartmental model (U-SEIR) integrating asymptomatic infection, super-spreading, and time-varying non-pharmaceutical interventions for the first wave of COVID-19[J]. Mathematical Biosciences and Engineering, 2026, 23(10): 3138-3168. doi: 10.3934/mbe.2026108
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