Multi-Phase Modeling for Vulnerability Detection & Patch Management: An Analysis Using Numerical Methods

Software systems are vulnerable to security breaches as they expand in complexity and functionality. The confidentiality, integrity, and availability of data are gravely threatened by flaws in a system’s design, implementation, or configuration. To guarantee the durability & robustness of the software, vulnerability identification and fixation have become crucial areas of focus for developers, cybersecurity experts and industries. This paper presents a thorough multi-phase mathematical model for efficient patch management and vulnerability detection. To uniquely model these processes, the model incorporated the notion of the learning phenomenon in describing vulnerability fixation using a logistic learning function. Furthermore, the authors have used numerical methods to approximate the solution of the proposed framework where an analytical solution is difficult to attain. The suggested systematic architecture has been demonstrated through statistical analysis using patch datasets, which offers a solid basis for the research conclusions. According to computational research, learning dynamics improves security response and results in more effective vulnerability management. The suggested model offers a systematic approach to proactive vulnerability mitigation and has important uses in risk assessment, software maintenance, and cybersecurity. This study helps create more robust software systems by increasing patch management effectiveness, which benefits developers, cybersecurity experts, and sectors looking to reduce security threats in a growing digital world.