<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-2807</article-id>
      <title-group>
        <article-title>Differential equation models of insider threat dynamics</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Thakur</surname>
            <given-names>Rahul</given-names>
          </name>
          <aff>Centre of Research Impact and Outcome (CRIO), Chitkara University, Rajpura, Punjab, 140417, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Goyal </surname>
            <given-names>Saumya</given-names>
          </name>
          <aff>Quantum University Research Center, Quantum University, Roorkee, Uttarakhand, 247667, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname> Wani</surname>
            <given-names>Tanveer  Ahmad</given-names>
          </name>
          <aff>Department of Physics, Noida International University, Greater Noida, Uttar Pradesh, 201312, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Karthick</surname>
            <given-names>Subramanian</given-names>
          </name>
          <aff>Department of Computer Engineering, Vishwakarma Institute of Technology, Pune, Maharashtra, 411037, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Balaji</surname>
            <given-names>D.</given-names>
          </name>
          <aff>Department of Humanities and Sciences, Aarupadai Veedu Institute of Technology, Vinayaka Mission’s Research Foundation (Deemed to be University), Paiyanur, Tamil Nadu, 603104, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Khasanova</surname>
            <given-names>Surayyo</given-names>
          </name>
          <aff>Department of Psychology and Medicine, Mamun University, Khiva, 220900, Uzbekistan</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Makhmudov</surname>
            <given-names>Samariddin</given-names>
          </name>
          <aff>Department of Finance and Tourism, Termez University of Economics and Service, Termez, 190111, Uzbekistan</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>10</issue>
      <fpage>2905</fpage>
      <lpage>2916</lpage>
      <pub-date date-type="pub">
        <day>27</day>
        <month>10</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>Insider threats are among the most complex cybersecurity threats as trusted employees can be intentional or unintentional threats to the organization. This study proposes a differential equation model of insider threat behavior as a representation of the dynamic interactions between trusted users, suspicious activity, compromised states and insider threat mitigation mechanisms. The proposed approach is a system of ODEs to describe the progression of threats, behavioral transitions, and the effect of monitoring and response strategies with time. Under different security conditions, the long-term behavior of the system is investigated by carrying out equilibrium and stability analyses. The numerical simulation results show the potential of the model for simulating threat escalation and assessing threat mitigation policies. The suggested mathematics-based modeling approach offers a quantitative basis for understanding the dynamics of insider threat, for a proactive assessment of risk, for making security decisions in complex organizations, and for formulating adaptable defense strategies against insider threat in 	cybersecurity.</p>
      </abstract>
      <kwd-group>
        <kwd>Insider threat dynamics</kwd>
        <kwd>Ordinary differential equations</kwd>
        <kwd>Cybersecurity modeling</kwd>
        <kwd>Stability analysis</kwd>
        <kwd>Numerical simulation</kwd>
        <kwd>Risk assessment</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
