In this study, we develop an SIQR epidemic network model incorporating individual feedback mechanisms, vaccination strategies, and quarantine measures. Through rigorous mathematical analysis, we derive the basic reproduction number R0 and establish that the disease-free equilibrium is globally asymptotically stable when R0 < 1, while the endemic equilibrium is globally asymptotically stable when R0 > 1. Utilizing optimal control theory, we prove the existence and uniqueness of the optimal control solution, which is obtained using Pontryagin’s minimum principle and Hamiltonian theory. This approach significantly reduces control costs and achieves efficient and cost-effective epidemic containment. Furthermore, the model optimizes the allocation of prevention and control resources under constrained conditions, enhancing control efficiency while alleviating socioeconomic burdens, thereby offering a sustainable framework for long-term epidemic management. Numerical simulations validate the model’s stability and the effectiveness of the optimal control strategy, demonstrating that vaccination and quarantine measures effectively suppress epidemic spread. These findings provide robust guidance for practical epidemic prevention and control, enabling health authorities and policymakers to implement targeted measures, such as prioritizing vaccine distribution, determining optimal coverage rates, and strategically planning quarantine zones and durations. Such measures effectively curb the transmission of infectious diseases and safeguard public health.
