On the dynamics of brucellosis infection in bison population with vertical transmission and culling.

We introduce a new mathematical modeling framework that seek to improve our quantitative understanding of the influence of chronic brucellosis and culling control on brucellosis dynamics in periodic and non-periodic environments. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. In addition, we also perform an optimal control study to explore optimal culling strategy in periodic and non-periodic environment.