Transmission dynamics of a multi-group brucellosis model with mixed cross infection in public farm

Brucellosis is one of the major public health problems in China, since there is a very large number of cattle and sheep. While the mixed feeding between cattle and sheep in public farm is one of the most typical characteristics in brucellosis outbreak regions, which has a large influence on the spreading of brucellosis. In this paper, we propose a multi-group SEIRV dynamical model with bidirectional mixed cross infection between cattle and sheep, and aim to investigate the influence of cross infection of mixed feeding on the brucellosis transmission. Firstly, we obtain the basic reproduction number R0R0, confirm the uniform existence and unique positive equilibrium of dynamic model when R0>1R0>1 and prove the global stability of endemic equilibrium when R0>1R0>1. In addition, sensitivity analysis of the infectious herds with different system in term of some parameter values are given. It is found that if there exists the bidirectional of mixed cross infection between cattle and sheep, the disease cannot disappear even though R01<1R01<1 and R02<1R02<1. These findings have important implication for brucellosis control: if we want to eliminate the brucellosis, firstly we should take measures to remove mixed cross infection, i.e., to prohibit mixed feeding.