Work

Stability, chaos and bifurcations by explicit criterions of a discrete tuberculosis epidemic model

Year: 2025

Type: article

Abstract: In this paper, we investigated the local stability, chaotic dynamics, and bifurcations of a discrete tuberculosis (TB) epidemic model, which provides crucial insights into the complex behavior of infectious disease spread in discrete-time settings. Specifically, we established the existence of a disease-free fixed point for all parametric values and demonstrated that an endemic fixed point emerges under specific parametric condition. The local stability at these fixed points was examined using the linear stability theory, revealing important thresholds for disease persistence or eradication. A comprehensive bifurcation analysis was conducted, showing that while no flip bifurcation occurred at the disease-free fixed point, both Neimark-Sacker and flip bifurcations took place at the endemic fixed point, and we studied said bifurcations by the explicit criterions. To further understand the model's nonlinear dynamics, we explored chaotic behavior by a feedback control strategy to mitigate chaotic oscillations. Numerical simulations are presented to validate our theoretical findings, demonstrating the model's capacity to capture real-world epidemiological patterns. Finally, theoretical results are also interpreted biologically/medically.

Source: AIMS Mathematics

DOI: 10.3934/math.2025762

Authors: Abdul Qadeer Khan, Raja Ramiz Ahmed Khan, Saud Fahad Aldosary

Institutions: University of Azad Jammu and Kashmir, Prince Sattam Bin Abdulaziz University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,200