Transmission dynamics of a Brucellosis model with incubation period

Abstract

Brucellosis is a major worldwide problem in public health. In this paper, we established and analyzed the Susceptible-Exposed-Infectious-Vaccinated for small ruminant–Susceptible-Exposed-Infectious-Vaccinated for cattle–Susceptible-Infectious-Recovered for human (SEIV–SEIV–SIR) model of Brucellosis with an incubation period which considered that human was infected through direct contact with infected humans, infected small ruminant, infected cattle and indirect contact with Brucella in the environment. The basic reproduction number [Formula: see text] of the model is computed by the spectral radius of the next-generation matrix. We proved that the disease-free equilibrium exists and we analyzed that the disease-free equilibrium point and endemic equilibrium point are global stability by constructing the [Formula: see text] function and applying the [Formula: see text] invariant principle. Numerical solutions and analytical reveal that the prevention and control measures for Brucella should be to detect infected livestock in time, reduce contact with infected livestock and increase the cure rate of infected humans.