Dynamic modeling and analysis of brucellosis on metapopulation network: Heilongjiang as cases

Abstract

Livestock transportation is a key factor that contributes to the spatial spread of brucellosis. To analyze the impact of sheep transportation on brucellosis transmission, we develop a human-sheep coupled brucellosis model within a metapopulation network framework. Theoretically, we examine the positively invariant set, the basic reproduction number, the existence, uniqueness, and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model. For practical application, using Heilongjiang Province as a case study, we simulate brucellosis transmission across 12 cities based on data using three network types: the BA network, the ER network, and homogeneous mixing network. The simulation results indicate that the network’s average degree plays a role in the spread of brucellosis. For BA and ER networks, the basic reproduction number and cumulative incidence of brucellosis stabilize when the network’s average degree reaches 4 or 5. In contrast, sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis, whereas transportation in a BA network helps to control it effectively. Furthermore, the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis. For cities with smaller sheep populations, such as Shuangyashan and Qitaihe, increasing the transport of sheep outward amplifies the spatial spread of the disease. In contrast, in cities with larger sheep populations, such as Qiqihar, Daqing, and Suihua, moderate sheep outflow can help reduce spread. In addition, cities with large livestock populations play a dominant role in the overall transmission dynamics, underscoring the need for stricter supervision in these areas.