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In this paper, based on SIR and SEIR epidemic models with a general nonlinear incidence rate, we incorporate time delays into the ordinary differential equation models. In particular, we consider two delay differential equation models in which delays are caused (i) by the latency of the infection in a vector, and (ii) by the latent period in an infected host. By constructing suitable Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, we prove the global stability of the endemic equilibrium and the disease-free equilibrium for time delays of any length in each model. Our results show that the global properties of equilibria also only depend on the basic reproductive number and that the latent period in a vector does not affect the stability, but the latent period in an infected host plays a positive role to control disease development.

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A nearly fully dense grade 300 maraging steel was fabricated by selective laser melting (SLM) additive manufacturing with optimum laser parameters. Different heat treatments were elaborately applied based on the detected phase transformation temperatures. Microstructures, precipitation characteristics, residual stress and properties of the as-fabricated and heat-treated SLM parts were systematically characterized and analyzed. The observed submicron grain size (0.31 μm on average) suggests an extremely high cooling rate up to 10 7 K/s. Massive needle-shaped nanoprecipitates Ni 3 X (X = Ti, Al, Mo) are clearly present in the martensitic matrix, which accounts for the age hardening. The interfacial relations between the precipitate and matrix are revealed by electron microscopy and illustrated in detail. Strengthening mechanism is explained by Orowan bowing mechanism and coherency strain hardening. Building orientation-based mechanical anisotropy, caused by 'layer-wise effect', is also investigated in as-fabricated and heat-treated specimens. The findings reveal that heat treatments not only induce strengthening, but also significantly relieve the residual stress and slightly eliminate the mechanical anisotropy. In addition, comprehensive performance in terms of Charpy impact test, tribological performance, as well as corrosion resistance of the as-fabricated and heat-treated parts are characterized and systematically investigated in comparison with traditionally produced maraging steels as guidance for industry applications.