Comprehensive mathematical model for assessing the resilience of primary healthcare organizations in response to global challenges and emergencies.

Ensuring the resilience of healthcare systems and medical organizations in the face of global challenges and emergencies is one of the key objectives of management. Despite a significant number of studies, there remains a lack of empirical data and effective tools for the quantitative analysis of the capacity of healthcare organizations to adapt to crises. This problem is particularly acute at the level of primary healthcare organizations, which play a critical role in maintaining the continuity of medical care delivery. The conditions arising from biological, technological, or military threats require primary healthcare providers to demonstrate a high degree of adaptability, readiness to handle surges in demand, and the ability to efficiently manage limited resources. In this regard, the development of approaches that enable the formalization and quantitative assessment of the resilience of healthcare organizations to various types of crises becomes a pressing scientific challenge. Objective. The aim of the study is to develop a comprehensive mathematical model for assessing the resilience of primary healthcare organizations in order to enhance their preparedness to respond to global challenges and emergencies. Materials and methods. The study was conducted in three stages, including a semantic analysis of resilience concepts, classification of global threats (biological, technological, and military), as well as the formalization of operational processes in primary healthcare organizations using methods of queuing theory, dynamic programming, linear integer programming, and calculated resilience indices for components such as patient flows, material and human resources, and standard operating procedures. Results. Eight models were developed, covering the dynamics of patient flows, optimization of appointment schedules, allocation of medical equipment, distribution of medical and nursing staff, as well as ensuring the stability of standard operating procedures. For each model, resilience indicators were defined, reflecting the ability of primary healthcare organizations to maintain operations under external impacts and crisis situations. The model enables the assessment of the impact of various types of emergencies and supports the selection of management strategies for adaptive response and recovery of operations. Conclusion. The proposed model provides a systematic and quantitatively justified approach to assessing the resilience of primary healthcare organizations in the context of global challenges and emergencies. Implementation of the model may facilitate the development of proactive management strategies, improve emergency preparedness, and support the rational allocation of resources.