摘要：We use a general autonomous discrete-time infectious disease model to extend the next generation matrix approach for calculating the basic reproduction number, R 0 , to account for populations with locally asymptotically stable period k cycles in the disease-free systems, where k ≥ 1 . When R 0 < 1 and the demographic equation (in the absence of the disease) has a locally asymptotically stable period k population cycle, we prove the local asymptotic stability of the disease-free period k cycle. That is, the disease goes extinct whenever R 0 < 1 . Under the same period k demographic assumption but with 1 , we prove that the disease-free period k population cycle is unstable and the disease persists. Using the Ricker recruitment function, we apply our results to discrete-time infectious disease models that are formulated for Susceptible-Infectious-Recovered (SIR) infections with and without vaccination, and Infectious Salmon Anemia Virus (ISA v ) infections in a salmon population. When 1 , our simulations show that the disease-free period k cycle dynamics drives the SIR disease dynamics, but not the ISAv disease dynamics.
关键词：Next generation matrix method ; Period k cycles ; Ricker recruitment ; R 0
