Modeling the Acceptance and Resistance of AI Tool Adoption in Higher Education: A Mathematical Modelling Approach

Timothy Ado Shamaki; PhD

doi:10.56201/ijcsmt.vol.12.no6.2026.pg56.72

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Modeling the Acceptance and Resistance of AI Tool Adoption in Higher Education: A Mathematical Modelling Approach

Timothy Ado Shamaki, PhD

Abstract

The rapid proliferation of artificial intelligence (AI) tools in academic settings has generated heterogeneous responses among university populations, ranging from enthusiastic adoption to firm resistance. Understanding the dynamics governing these contrasting attitudes is essential for designing effective institutional policies, digital infrastructure, and awareness campaigns. In this paper, we propose and analyse a deterministic compartmental mathematical model that partitions a university population into four mutually exclusive classes, namely: Non-users ( N ), Moderate users (M ), Active users ( A ), and Resistant users ( R ). The model uniquely incorporates both endogenous peer-driven social contagion and continuous, uninterrupted exogenous digital media and internet exposure intensity ( 0 I ). Because digital/social media exerts a constant force of adoption, the system lacks a traditional adoption-free threshold. We analyze the model under persistent internet drive, proving the existence and uniqueness of a permanent coexistence equilibrium ( * E ) using stability analysis. We establish the global asymptotic stability of this persistent state via a non-linear Lyapunov function construction. Numerical simulations validate the analytical findings, illustrating how varying internet penetration levels scale user saturation and providing actionable insights for university administrators.

Keywords

AI adoption; mathematical modelling; compartmental model; continuous internet drive; global asymptotic stability; Lyapunov function; sensitivity analysis.

References

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Modeling the Acceptance and Resistance of AI Tool Adoption in Higher Education: A Mathematical Modelling Approach

Abstract

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