Bifurcation analysis of an influenza A (H1N1) model with treatment and vaccination.

Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet ISSN: 1932-6203 (Electronic) Linking ISSN: 19326203 NLM ISO Abbreviation: PLoS One Subsets: MEDLINE

Original Publication: San Francisco, CA : Public Library of Science

Influenza, Human*/epidemiology ; Influenza, Human*/prevention & control ; Influenza, Human*/transmission ; Influenza A Virus, H1N1 Subtype* ; Vaccination*; Humans ; Mexico/epidemiology ; Colombia/epidemiology ; Influenza Vaccines ; Basic Reproduction Number ; Computer Simulation ; Models, Theoretical

This research uses numerical simulations and mathematical theories to simulate and analyze the spread of the influenza virus. The existence, uniqueness, positivity, and boundedness of the solution are established. We investigate the fundamental reproduction number guaranteeing the asymptotic stability of equilibrium points that are endemic and disease-free. We also examine the qualitative behavior of the models. Using the Lyapunov method, Routh-Hurwitz, and other criteria, we explore the local and global stability of these states and present our findings graphically. Our research assesses control policies and proposes alternatives, performing bifurcation analyses to establish prevention strategies. We investigate transcritical, Hopf, and backward bifurcations analytically and numerically to demonstrate disease transmission dynamics, which is novel to our study. Contour plots, box plots, and phase portraits highlight key characteristics for controlling epidemics. The disease's persistence depends on its fundamental reproduction quantity. To validate our outcomes, we fit the model to clinical data from influenza cases in Mexico and Colombia (October 1, 2020, to March 31, 2023), aiming to analyze trends, identify critical factors, and forecast influenza trajectories at national levels. Additionally, we assess the efficacy of implemented control policies.
Competing Interests: The authors have declared that no competing interests exist.
(Copyright: © 2025 Mohammad et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

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0 (Influenza Vaccines)

Date Created: 20250106 Date Completed: 20250106 Latest Revision: 20250108

20250114

PMC11703119

10.1371/journal.pone.0315280

39761238