Deterministic and Stochastic Gompertz Prey-Predator Model for the Effect of Thymoquinone on Oral Squamous Carcinoma Cell Lines (HSC-4)

Authors

  • Shabana Tabassum Mathematics and Statistics Missouri University of Science and Technology. 202 Rolla Building, 400 W. 12th St., Rolla, MO 65409-0020, USA
  • Norhayati Rosli Centre for Mathematical Sciences, Universiti Malaysia Pahang Al-Sultan Abdullah, Lebuh Persiaran Tun Khalil Yaakob, 26300 Kuantan, Pahang, MALAYSIA https://orcid.org/0000-0001-5493-2629
  • Wastuti Hidayati Suriyah Faculty of Dentistry, Universitas YARSI, Jl. Let. Jend. Suprapto Kav. 13. Jakarta 10510, INDONESIA https://orcid.org/0000-0002-0720-3279
  • Solachuddin Jauhari Ichwan Arief PAPRSB Institute of Health Sciences, Universiti Brunei Darussalam, Jalan Tungku Link, Gadong BE1410, BRUNEI https://orcid.org/0000-0002-6965-0840

DOI:

https://doi.org/10.22452/mjs.vol45sp2.7

Keywords:

Deterministic model, stochastic model, thymoquinone, oral cancer

Abstract

Oral squamous cell carcinoma (OSCC) is one of the most common malignancies affecting the head and neck region. Thymoquinone (TQ), the primary bioactive compound of black seed (Nigella sativa), has shown antineoplastic properties in various tumor cell types. However, research on TQ effects in tumor cell models, particularly OSCC, remains at an early stage. TQ, a phytochemical with confirmed anticancer potential, has been shown to inhibit OSCC progression mainly through induction of apoptosis. In this study, a prey–predator stochastic Gompertz model is used to characterize the dynamics of the HSC-4 OSCC cell line in response to TQ treatment. The model is first formulated as an ordinary differential equation (ODE), then extended to a stochastic differential equation (SDE) to capture biological noise arising from intrinsic and extrinsic sources within the cellular environment. The Markov Chain Monte Carlo (MCMC) method is utilized to estimate the model’s kinetic parameters, while fourth-order stochastic Runge-Kutta (SRK4) algorithms are applied for numerical simulation. Model outputs are validated against in vitro experimental data from TQ-treated HSC-4 cells. The deterministic framework is analyzed in terms of the positivity of solutions and equilibrium states, including the disease-free equilibrium (DFE), the treatment-failure equilibrium (TFE), and the successful treatment equilibrium (SFE). The root mean-square error (RMSE) is computed to assess the consistency between simulated outcomes and experimental observations. The findings demonstrate the model's capability in capturing and explaining the dynamic behavior of HSC-4 cells under TQ treatment.

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Published

15-11-2026

Issue

Vol. 45 No. Sp2 (2026): Special Issue: 5th International Conference on Applied & Industrial Mathematics and Statistics 2025 (ICoAIMS 2025)

Section

Special Issue - 5th ICoAIMS 2025

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