A Brucellosis Model with Different Clinical Symptoms and a Time Delay Representing Incubation Period: Global Dynamics and Data Fitting

Abstract

Brucellosis is a significant zoonotic disease that has a high incidence rate in sheep, particularly in the Inner Mongolia region of China. To better investigate its transmission dynamics, this paper proposes a sheep brucellosis model incorporating acute and chronic infections, a saturated incidence rate describing environmental transmission and a time delay representing the incubation period. By constructing Lyapunov functionals and using LaSalle’s invariance principle, it is shown that the global dynamics of the disease is completely determined by the basic reproduction number: If $\mathcal{R}_0<1,$ the brucellosis always dies out; if $\mathcal{R}_0>1,$ a unique endemic equilibrium exists and is globally asymptotically stable. Using data of sheep brucellosis cases in Inner Mongolia from 2016 to 2020, unknown parameters and the basic reproduction number $(\mathcal{R}_0=1.544)$ are estimated via the Markov chain Monte Carlo method. Numerical simulations show that reducing the transmission rate of acutely infected sheep while increasing the culling rate of symptomatic infected sheep is the most effective strategy to control the spread of brucellosis in Inner Mongolia. Notably, decreasing the proportion of acutely infected sheep or increasing acute-to-chronic conversion rate may lead to a significant short-term increase in chronically infected sheep.