A Mathematical Model for Ovine Brucellosis during Dynamic Transportation of Sheep, and Its Applications in Jalaid Banner and Ulanhot City

Abstract

Brucellosis a the serious infectious disease in Hinggan League. Research has demonstrated that a large amount of transportation is one of the main reasons for so many cases. However, the specific transmission mechanism of brucellosis is not clear. In this paper, we utilize a multi-patch model to study the effect of the transportation of sheep on the spread of brucellosis in Hinggan League. Theoretically, we prove the global stability of the disease-free equilibrium and the uniform persistence of the endemic equilibrium. In a practical application, we apply the model to investigate the spread of brucellosis in Ulanhot city and Jalaid Banner, which are geographically adjacent in Hinggan League. The strains carried by humans are B.melitensis bv.1 and B.melitensis bv.3. We use the two-patch model to fit reported brucellosis cases data of two places by Markov Chain Monte Carlo (MCMC) simulations. It is found that the global basic reproduction number R0 is larger than 1, but the isolated basic reproduction numbers in Ulanhot city and Jalaid Banner are both less than 1. This indicates that the prevalence of brucellosis may be caused by the transportation of sheep. Sensitivity analysis of parameters on R0 shows that it is the most effective means to control the transportation of sheep from Jalaid to Ulanhot on preventing brucellosis. Moreover, we also discover that improving vaccine efficiency is an effective method compared with strengthening the vaccination coverage rate and improving the detection rate of sheep with brucellosis. Our dynamic behavior analysis of the two-patch model can provide a reference for the dynamic behavior analysis of the n-patch model, and our results provide a guide for how to control brucellosis based on transportation.