A study of fractional bovine tuberculosis model with vaccination on human population

Abstract

A bacterial and zoonotic disease called bovine tuberculosis (bTB) can be contracted by breathing in aerosols, consuming unpasteurized milk, or eating raw meat. The evolution of bovine tuberculosis transmission in both human and animal populations is investigated in this research using a fractional order model with caputo sensing and a compartment for human vaccination. The threshold quantity R₀ was also constructed using Volterratype Lyapunov functions, LaSalle’s invariance principle, and the Routh-Hurwitz criterion to identify the sick state and provide conditions that guarantee the local and global asymptotic stability of the equilibria. In order to determine the variables that control the dynamics of bTB, we performed a sensitivity study. The analysis indicates that factors influencing the spread of bTB include the rate of environmental contamination, the rate of bTB transmission from animal to animal, and the rate at which bTB is contracted by people from infected animals and the environment. However, the disease becomes less common in humans as vaccination rates rise and consumption of the contaminated environment’s products (meat and dairy products) declines. For the management of bTB, it is recommended to implement educational initiatives, monitor the environment, treat affected individuals, administer immunizations, and confine contaminated animals. Numerical experiments are used to show how useful the found theoretical results are.