Mathematical modelling of COVID-19 transmission dynamics with immigration and dual quarantine–isolation strategies

The COVID-19 pandemic remains a major global health challenge, particularly in low– and middle–income countries where healthcare capacity is limited and individual health-seeking behaviour strongly influences transmission dynamics. Motivated by this context, we formulate and analyze a deterministic compartmental model that incorporates dual intervention pathways—government-managed and personally adopted quarantine and isolation—together with immigration of exposed and infectious individuals and return-to-susceptible dynamics. The basic reproduction number B 0 is derived and its dependence on key epidemiological and intervention parameters is investigated through sensitivity analysis. Numerical simulations, calibrated using early outbreak data from Nigeria, demonstrate how the interaction between quarantine, isolation, and mobility shapes epidemic trajectories under varying levels of compliance. Sensitivity results reveal that transmission intensity, natural mortality, and susceptible recruitment exert the strongest influence on B 0 , while both government and personal isolation significantly mitigate transmission when effectively implemented. These results highlight the importance of accounting for heterogeneous behavioural responses and multi-route interventions in mathematical models of COVID-19, especially in resource-constrained settings. The proposed framework therefore provides modelling insights that can support the design and evaluation of context-specific control strategies for COVID-19 and other emerging infectious diseases.