A two-patch model to quantify uncertainties in the transmission of brucellosis between domestic animals

Brucellosis, a neglected zoonotic disease, poses significant health risks to both humans and livestock. This study investigates a key factor influencing brucellosis transmission: the movement of animals in and out of communal grazing areas. We develop a Continuous Time Markov Chain (CTMC) stochastic model, building on its deterministic counterpart, to assess the impact of short-term animal movements on disease transmission dynamics. By incorporating stochasticity, the model captures the inherent variability in disease transmission and animal movements, providing deeper insights than traditional deterministic models. A multitype branching process is employed to evaluate the probabilities of disease extinction. We compute the basic reproduction number ( R 0 ) and the stochastic threshold ρ ( M ) . Numerical simulations indicate that brucellosis transmission accelerates when domestic animals spend more time in high-risk communal grazing areas. Additionally, the results suggest a high probability of disease extinction when animals moves out of high-risk area. Conversely, when animals from both patches increase their time in high-risk zones, the likelihood of disease extinction diminishes. This study underscores the importance of implementing strategic movement controls and targeted interventions in high-risk areas to mitigate outbreaks and enhance disease management.