A two-stage sheep-environment coupled brucellosis transmission dynamic model: Stability analysis and optimal control
Shuangjie Bai, Boqiang Cao, Ting Kang, Qingyun Wang
Abstract
Brucellosis is a zoonotic disease that poses a severe threat to public health security. The study of the transmission patterns and control strategies of brucellosis has become a hot topic in fields such as animal husbandry and biomathematics. To this end, we constructe a two-stage sheep-environment coupled transmission dynamics model based on the transmission characteristics of brucellosis. First, the basic reproduction number is calculated, with the result that the global stabilities of disease-free and endemic equilibria are acquired, respectively. Subsequently, an optimal control problem is addressed following Pontryagin's maximum principle considering the slaughter of infected sheep and the reduction of brucella emission into the environment. Finally, numerical simulations are used to validate the accuracy of theoretical results. In addition, the sensitivities of some major parameters and the impacts of different control strategies on brucellosis transmission are also investigated, the results reveal that any control strategy can control the transmission of brucellosis to a certain extent, but mixed control is more beneficial to reduce the number of exposed sheep, infected sheep, and brucellosis in environment.