Evaluating lung cancer control through a time-delay mathematical model with detailed sensitivity analysis

Authors

  • Shah Zeb
    School of Distance Education, Universiti Sains Malaysia, USM, 11800 Penang, Malaysia
  • Awais Ahmad
    Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
  • Rizwana Kausar
    School of Biological Sciences, Universiti Sains Malaysia, Minden, USM, 11800 Penang, Malaysia
  • Siti Ainor Mohd Yatim
    School of Distance Education, Universiti Sains Malaysia, USM, 11800 Penang, Malaysia
  • Nurulhuda Ramli
    School of Distance Education, Universiti Sains Malaysia, USM, 11800 Penang, Malaysia
  • Muhammad Rafiq
    School of Biological Sciences, Universiti Sains Malaysia, Minden, USM, 11800 Penang, Malaysia dDepartment of Mathematics, Namal University, 30 km Talagang Road, Mianwali 42250, Pakistan

Keywords:

Lung cancer, Basic reproduction number, Sensitivity analysis, Existence and uniqueness, Nonstandard finite difference

Abstract

Lung cancer (LC) is a leading cause of cancer-related deaths worldwide, posing a significant threat to public health due to its complex development, late diagnosis, and poor response to treatment. Rising rates, particularly among those exposed to tobacco consumption and environmental pollution, highlight the need for a realistic interpretation of disease dynamics through mathematical modeling. In this study, a nonlinear dynamical model of LC with time delay is formulated to represent the lag associated with smoking exposure and the evolution of smoking-related effects. The delay acts specifically through the delayed smoking-exposure interaction terms and does not represent treatment or immune response. The model is analyzed to confirm that solutions remain positive and bounded, ensuring biological feasibility. The basic reproduction number is calculated to describe threshold dynamics, and local stability of both the disease-free and endemic equilibrium is examined. Sensitivity analysis identifies the parameters influencing the model threshold quantity. The displayed analysis shows positive effects of theta, a, b, and e on Re0 and negative effects of d, g, m, and tau. These signs describe the mathematical sensitivity of the threshold quantity and do not establish treatment or recovery effects. Numerical simulations using nonstandard finite difference (NSFD), Euler, and fourth-order Runge--Kutta (RK4) methods validate the analytical results, with NSFD proving to be more stable and dynamically consistent. Findings suggest that government interventions, including tobacco control, education, and early screening awareness, can reduce the disease burden. These results offer insights for policymakers to develop cost-effective strategies. 

Dimensions

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Published

2026-08-10

How to Cite

Evaluating lung cancer control through a time-delay mathematical model with detailed sensitivity analysis. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3539. https://doi.org/10.46481/jnsps.2026.3539

Issue

Volume 8, Issue 3, August 2026 (In Progress)

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 Shah Zeb, Awais Ahmad, Rizwana Kausar, Siti Ainor Mohd Yatim, Nurulhuda Ramli, Muhammad Rafiq (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Evaluating lung cancer control through a time-delay mathematical model with detailed sensitivity analysis. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3539. https://doi.org/10.46481/jnsps.2026.3539

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