Modeling and optimal control analysis of age-structured Brucellosis under environmental transmission with vaccination and culling

Brucellosis is currently recognized as one of the most serious zoonotic infectious diseases, caused by Brucella abortus, and is classified by the World Organization for Animal Health as a Category B zoonotic disease. In this study, we developed a new seven-compartment model of the transmission dynamics brucellosis in sheep, which accounts for the combined effects of vaccination, age structure, culling of infected sheep, and the impact of the contaminated environment. Our analysis demonstrates that the DFE point of the system is globally and asymptotically stable when the basic reproduction number $ R_0 < 1 $. Furthermore, we show that the disease persists when $ R_0 > 1 $, in accordance with the theory of uniform persistence. In the numerical simulation section, we fit data on the number of Brucella infections in sheep in Egypt from 1999 to 2010 and estimate the model's parameters using the least squares method. Based on this, we propose four control strategies to establish the optimal control system. We applied Pontryagin's maximum principle to derive the necessary conditions for optimal control and perform numerical simulations. A cost-benefit analysis was conducted from the perspective of sheep farmers. Our findings suggest that the most cost-effective strategy for reducing brucellosis infection rates in sheep is to uniformly house young sheep and vaccinate them simultaneously.