It is widely acknowledged that flies are crucial contributors in the transmission of anthrax, yet their mechanical transmission function as spore vectors has rarely been investigated using mathematical modeling approaches. This work incorporates their dual roles of biting and mechanical transmission into a mathematical framework, establishing a periodic partially degenerate reaction-diffusion model, where fly-mediated spore dispersal (mechanical transmission) is described through a nonlocal term. Due to the degenerate characteristic (partial absence of diffusion terms), we first examine the smoothness property of the solution mapping. Then we demonstrate that the periodic mapping is \(\alpha\) -contracting. Subsequently, the basic reproduction number \(R_{0}\) is introduced, and its role as a threshold parameter in disease persistence is confirmed. Our analytical exploration of the non-periodic case establishes that under specific conditions, nonlocal spore transport does not increase \(R_{0}\) nor escalate transmission risk. Numerical simulations further clarify how fly-mediated spore dispersal affects anthrax dynamics. Our results show that flies exhibit a spatial averaging effect during transport, and this effect depends non-monotonically on the dispersal distance. As a result, \(R_{0}\) also changes non-monotonically with transport distance, suggesting a dual role of mechanical transmission: short-distance transport tends to increase transmission, whereas sufficiently large transport distances may reduce it. The robustness of this non-monotonic relationship for \(R_{0}\) is supported by uncertainty analysis, sensitivity analysis, and comparisons with different kernel functions. This suggests that the observed pattern is robust within the modeling framework. Collectively, these results improve the understanding of the mechanisms of spatial anthrax transmission. Threshold dynamics
