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An infectious disease model with two dis-tributed delays is proposed to incorporate both the latency of the infection in a vector and the latent period in an infected host. The basic reproduction number TZo is defined and shown to give a sharp threshold. Specifically, if Ro < 1, then the disease-free equilibrium is globally asymptotically stable and the disease dies out; whereas if Ro > 1, then a Lyapunov func-tional is used to prove that the endemic equilibrium is globally asymptotically stable, thus the disease persists at an endemic level. This model includes and extends several delay models in the literature. [ABSTRACT FROM AUTHOR]

We investigate an SIR compartmental epiclemic model in a patchy environment where individuals in each compartment can travel among Ii patches. We derive the basic reproduction number R0 and prove that, if R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable. In the case of R0 > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. [ABSTRACT FROM AUTHOR]