Numerical Study of the Dynamics of Medical Data Security in Information Systems

Mukhammejanova D. Mukasheva A. Chen S.
January 2026 Multidisciplinary Digital Publishing Institute (MDPI)

Computers
2026 #15 Issue 1

Background: Integrated medical information systems process large volumes of sensitive clinical data and are exposed to persistent cyber threats. Artificial intelligence (AI) is increasingly used for anomaly detection and incident response, yet its systemic effect on the dynamics of security indicators is not fully quantified. Aim: To develop and numerically study a nonlinear dynamical model describing the joint evolution of system vulnerability, threat activity, compromise level, AI detection quality, and response resources in a medical data protection context. Method: A five-dimensional system of ordinary differential equations was formulated for variables (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.). Parameters characterize appearance and elimination of vulnerabilities, attack intensity, AI learning and degradation, and resource consumption. The corresponding Cauchy problem (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) was solved on (Formula presented.) numerically using a fourth-order Runge–Kutta method. Results: Numerical modelling showed convergence to a favourable steady regime. On the interval t ∈ [195, 200] the mean values were (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.). Thus, the initial 10% compromise is reduced by more than 99.9%, while AI detection quality stabilizes at around 0.58, and response capacity increases 25-fold. Conclusions: The model quantitatively confirms that the integration of AI detection and a managed response capacity enables the system to reach a stable state with virtually zero compromised medical data even with non-zero threat activity.

healthcare information system , incident detection , medical data , nonlinear dynamical system , numerical simulation , ordinary differential equations

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Faculty of Information Technology, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Faculty of Information Technology, International Information Technology University, Almaty, 050040, Kazakhstan
School of Information Technology and Engineering, Kazakh-British Technical University, Almaty, 050000, Kazakhstan
School of Data Science, Fudan University, Shanghai, 200433, China

Faculty of Information Technology
Faculty of Information Technology
School of Information Technology and Engineering
School of Data Science

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