Two-group SEIQR epidemiological model with heterogeneous behavior

The spread of COVID-19 is strongly influenced by heterogeneity in population behavior and contact patterns. Understanding how these differences affect transmission and control strategies is essential for designing effective interventions. We develop a two-group SEIQR epidemiological model that distinguishes between high- and low-risk populations. The model is analyzed to establish positivity, boundedness, and global existence of solutions. The basic reproduction number \(R_0\) is derived using the next-generation matrix, and global stability of both disease-free and endemic equilibria is established under a symmetry condition on transmission rates. A global sensitivity analysis using the LHS-PRCC method is conducted. An optimal control framework incorporating time-dependent vaccination and awareness interventions is formulated using Pontryagin’s Maximum Principle. The sensitivity analysis identifies the within low-risk transmission coefficient \( \beta_{11} \) as the strongest driver increasing \(R_0\) , while the low-risk quarantine rate \( q_1 \) has the greatest impact in reducing it. Numerical simulations show that awareness-based interventions are highly effective in early epidemic stages, while combined vaccination and awareness strategies achieve the best performance in reducing infections and overall cost. Under the transmission matrix, epidemiological parameters, and objective-function weights considered in this study, the optimal control solution allocates greater intervention effort to the low-risk group. The results demonstrate that heterogeneity in transmission can substantially influence the optimal allocation of interventions between population groups. The greater allocation to the low-risk group observed in this study is a model-dependent finding and should not be interpreted as general public-health guidance to prioritize low-risk populations over clinically high-risk populations.