Abstract

In this paper, we propose a novel dynamical model on time scales consisting of new parameters to investigate the transmission dynamics of tuberculosis (TB), one of the deadliest infectious diseases worldwide, characterized by a long latency stage. The dynamical TB model, governed by the Susceptible–Exposed–Infected–Recovered (SEIR) framework within a unified form, yields a continuous model with a non-saturated incidence rate on the real numbers and discrete models with saturated incidence rates when different time domains are chosen. We analyze the stability of the equilibrium points of both the continuous TB model on the set of real numbers and the discrete TB model defined on the set of numbers separated by h, where the basic reproduction number determines whether an outbreak occurs or the disease dies out. In addition, we demonstrate the significance of the discrete TB model through a numerical analysis guided by our mathematical results and previously estimated parameters from earlier Philippine and South Korea TB data. Through this analysis, we emphasize how the model parameters, particularly the time step h, influence the disease dynamics and lead to biologically relevant results. Our modeling approach and mathematical analysis underline that time scales models can be used to generate novel continuous and discrete models, which are not mere discretization's of a continuous model, and can include new parameters that meaningfully represent practical settings such as data frequency.

Department(s)

Mathematics and Statistics

Publication Status

Full Text Access

Keywords and Phrases

Dynamical systems; Mathematical modeling; Time scale; Tuberculosis

International Standard Serial Number (ISSN)

0378-4754

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Elsevier, All rights reserved.

Publication Date

01 Mar 2026

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