The Delta and Omicron variants drove the two most consequential COVID-19 waves in the region, yet no existing multi-strain compartmental model combines rigorous stability analysis with modern, uncertainty-quantified parameter estimation for this pair. We addressed this gap through four contributions. First, we formulated a deterministic two-strain SVE$ _i $A$ _i $I$ _i $JHR model with eleven compartments and established positivity, boundedness, closed-form variant-specific reproduction numbers $ \mathcal{R}_{0i} $ (evaluated under the baseline intervention configuration), and the local stability and a conditional global-stability result for the disease-free equilibrium via a Castillo-Chavez-Song decomposition, together with the existence of the single-variant endemic equilibria and their local stability under explicit Routh-Hurwitz and invasion conditions, together with a numerical threshold-branch analysis illustrating the forward exchange of stability at the epidemic threshold. Second, we introduced a three-stage hybrid estimation pipeline—lsqnonlin, a deterministic physics-informed neural network (PINN) embedding the full eleven ordinary differential equation (ODE) residual, and a long short-term memory (LSTM) residual-correction module—calibrated against Delta- and Omicron-wave surveillance data. Third, we extended the physics-informed neural network (PINN) to a Bayesian PINN via Hamiltonian Monte Carlo simulation, yielding $ 95\% $ credible intervals for all six learned parameters and for $ \mathcal{R}_{0i} $ ($ \mathcal{R}_{01} = 1.87 $, $ \mathcal{R}_{02} = 1.64 $), providing uncertainty quantification absent from prior multi-strain COVID-19 models for this setting. Propagating literature uncertainty in the fixed parameters $ \alpha, \eta_i $ jointly with the learned parameters widens these credible intervals substantially and can bring them below unity. Fourth, local and global sensitivity analyses and a counterfactual efficacy-coverage scenario analysis showed that vaccine efficacy is the single most influential controllable parameter and that, under the proportional intervention scenario, Delta is the more restrictive variant, with a conditional proportional-intervention benchmark of $ 59.6\% $ (posterior-based $ 95\% $ interval: $ [56.0\%, 64.6\%] $) at the reported operating efficacies. This benchmark is not a full-model herd-immunity threshold. The hybrid PINN-LSTM framework reduces $ 30 $-day forecast root mean square error (RMSE) by about $ 23\% $ over PINN-only and $ 40\% $ over lsqnonlin.
Citation: Mallela Ankamma Rao, Nazek Alessa, Medisetty Padma Devi, Carlos Martin-Barreiro, Prasantha Bharathi Dhandapani. A two-strain Delta-Omicron COVID-19 model: stability and physics-informed parameter estimation[J]. AIMS Mathematics, 2026, 11(10): 34468-34530. doi: 10.3934/math.20261344
The Delta and Omicron variants drove the two most consequential COVID-19 waves in the region, yet no existing multi-strain compartmental model combines rigorous stability analysis with modern, uncertainty-quantified parameter estimation for this pair. We addressed this gap through four contributions. First, we formulated a deterministic two-strain SVE$ _i $A$ _i $I$ _i $JHR model with eleven compartments and established positivity, boundedness, closed-form variant-specific reproduction numbers $ \mathcal{R}_{0i} $ (evaluated under the baseline intervention configuration), and the local stability and a conditional global-stability result for the disease-free equilibrium via a Castillo-Chavez-Song decomposition, together with the existence of the single-variant endemic equilibria and their local stability under explicit Routh-Hurwitz and invasion conditions, together with a numerical threshold-branch analysis illustrating the forward exchange of stability at the epidemic threshold. Second, we introduced a three-stage hybrid estimation pipeline—lsqnonlin, a deterministic physics-informed neural network (PINN) embedding the full eleven ordinary differential equation (ODE) residual, and a long short-term memory (LSTM) residual-correction module—calibrated against Delta- and Omicron-wave surveillance data. Third, we extended the physics-informed neural network (PINN) to a Bayesian PINN via Hamiltonian Monte Carlo simulation, yielding $ 95\% $ credible intervals for all six learned parameters and for $ \mathcal{R}_{0i} $ ($ \mathcal{R}_{01} = 1.87 $, $ \mathcal{R}_{02} = 1.64 $), providing uncertainty quantification absent from prior multi-strain COVID-19 models for this setting. Propagating literature uncertainty in the fixed parameters $ \alpha, \eta_i $ jointly with the learned parameters widens these credible intervals substantially and can bring them below unity. Fourth, local and global sensitivity analyses and a counterfactual efficacy-coverage scenario analysis showed that vaccine efficacy is the single most influential controllable parameter and that, under the proportional intervention scenario, Delta is the more restrictive variant, with a conditional proportional-intervention benchmark of $ 59.6\% $ (posterior-based $ 95\% $ interval: $ [56.0\%, 64.6\%] $) at the reported operating efficacies. This benchmark is not a full-model herd-immunity threshold. The hybrid PINN-LSTM framework reduces $ 30 $-day forecast root mean square error (RMSE) by about $ 23\% $ over PINN-only and $ 40\% $ over lsqnonlin.
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Figures(18) / Tables(11)
Mallela Ankamma Rao, Nazek Alessa, Medisetty Padma Devi, Carlos Martin-Barreiro, Prasantha Bharathi Dhandapani. A two-strain Delta-Omicron COVID-19 model: stability and physics-informed parameter estimation[J]. AIMS Mathematics, 2026, 11(10): 34468-34530. doi: 10.3934/math.20261344
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