Impact of Vaccination on Influenza Disease Transmission in Humans and Birds: Sensitivity and Bifurcation Analysis within Fractional Framework
Year: 2026
Type: article
Abstract: Avian influenza is a zoonotic disease that spreads from birds to humans through viral infection and poses a substantial threat to the poultry industry, which can result in severe financial consequences as well as serious public health concerns for the community. To control the spread of avian influenza, effective control measures such as vaccination are important. In order to highlight the influence of the vaccine on infected humans and birds, this study formulates a novel fractal-fractional avian influenza model in the Mittag-Leffler sense. We perform comprehensive qualitative and quantitative analysis, including verification of the presence of a single solution, positivity and boundedness of solutions, influenzafree and existing equilibrium points, the threshold parameter R0, the local and global stability of the influenza-free equilibrium points, the presence of forward transcritical bifurcation, and the local and global sensitivity analysis. Through local and global stability of Influenza-free equilibrium points, we verify that infection in birds stops and the chances of Influenza spread decrease when R0 < 1, while outbreaks and human transmission are possible when R0 > 1. We provide statistical analysis to show the symmetric behaviour of the compartments and the chaos test to reveal the bounded nature of all compartments of the model. In order to obtain numerical solutions, we derive a numerical technique based on Newton polynomials. We provide the phase plots illustrating the interactions between the human and bird compartments. The sensitivity analysis identifies transmission rate, recruitment, vaccination, and recovery as the most influential factors in controlling avian influenza. Through the zoonotic transmission pathway, these measures not only stabilize the bird population but also provide indirect protection to the human population.
Authors: Usama Atta, Aqeel Ahmad, Sadia Sattar
Institution: Ghazi University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7203770075