Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold

• Main Authors: Wei Zhang, Juan Zhang, Yong-Ping Wu, Li Li
• Format: Article
• Language: English
• Published: Hindawi-Wiley 2019-01-01
• Series: Complexity
• Online Access: http://dx.doi.org/10.1155/2019/6526589

As we all know, bacteria is different from virus which with certain types can be killed by the immune cells in the body. The brucellosis, a bacterial disease, can invade the body by indirect transmission from environment, which has not been researched by combining with immune cells. Considering the effects of immune cells, we put a minimum infection dose of brucellosis invading into the dairy cows as an immunological threshold and get a switch model. In this paper, we accomplish a thorough dynamics analysis of a SEIB switch model. On the one hand, we can get a disease-free and bacteria-free steady state and up to three endemic steady states which may be thoroughly analyzed in different cases of a minimum infection dose in a switch model. On the other hand, we calculate the basic reproduction number R0 and know that the disease-free and bacteria-free steady state is a global stability when R0<1, and the one of the endemic steady state is a conditionally global stability when R0>1. We find that different amounts of R0 may lead to different steady states of brucellosis, and considering the effects of immunology is more serious in mathematics and biology.