Emerging infectious disease dynamics with compliance and isolation resource constraints

The effectiveness of isolation strategies against emerging infectious diseases (EIDs) is critically undermined by two interacting factors: Limited resource capacity and imperfect public compliance, yet their combined impact remains poorly quantified. We develop an ordinary differential equation (ODE) model incorporating a saturation function for resource limits and a compliance parameter ($ \epsilon $) to quantify their nonlinear interaction. Theoretical analysis reveals a resource-driven backward bifurcation, indicating that reducing a basic reproduction number $ R_0 $ below 1 is necessary but may be insufficient for disease elimination when isolation capacity is critically low. Numerically, we identify a counterintuitive paradox: High compliance amplifies the infection risk when isolation resources are severely constrained. The simulation results classify the dynamic regimes under various parameter settings and reveal the qualitative impact of different isolation strategies. The study finds that increasing isolation resources, combined with a certain level of compliance, significantly reduces the infection risk and aids in disease control. Notably, specific transmission patterns emerge when isolation resources are inadequate, resulting in elevated infection risks even when compliance is high. Our results underscore the imperative of synchronizing resource allocation with behavioral interventions, particularly during early outbreak stages, providing a framework for precision public health strategies.