In the evolving landscape of computing environments, fog computing has emerged as a pivotal technology for handling the increasing demands of Internet of Things (IoT) applications. Fog computing, with its decentralized approach, brings computational power closer to IoT devices, reducing latency and bandwidth constraints. However, this distributed architecture poses significant cybersecurity challenges, necessitating a holistic mathematical model to ensure the security and integrity of fog resources. This review presents a comprehensive mathematical cyber security model that is tailored to fog resource management in computing environments. The models generally encompass a wide array of security aspects, including data confidentiality, integrity, availability, and authentication. Leveraging advanced mathematical techniques, the models offer a robust framework for assessing and enhancing security in fog computing systems. The key components include threat modeling, risk assessment, and dynamic resource allocation strategies. By systematically analyzing potential threats and vulnerabilities specific to fog computing, these models assist in devising effective countermeasures and security policies. Moreover, there is a need to incorporate an adaptive resource allocation algorithm to dynamically allocate computing resources based on security priorities and real-time threat assessments. This review demonstrates the effectiveness of the mathematical cyber security model in bolstering the resilience of fog computing environments. The review highlights the need for safeguarding the next generation of fog computing systems against cyber threats, fostering the continued growth and adoption of transformative technology.