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Age structured discrete-time disease models with demographic population cycles

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We use juvenile-adult discrete-time infectious disease models with intrinsically generated demographic population cycles to study the effects of age structure on the persistence or extinction of disease and the basic… Click to show full abstract

We use juvenile-adult discrete-time infectious disease models with intrinsically generated demographic population cycles to study the effects of age structure on the persistence or extinction of disease and the basic reproduction number, . Our juvenile-adult Susceptible-Infectious-Recovered (SIR) and Infectious-Salmon Anemia-Virus (ISA models share a common disease-free system that exhibits equilibrium dynamics for the Beverton-Holt recruitment function. However, when the recruitment function is the Ricker model, a juvenile-adult disease-free system exhibits a range of dynamic behaviours from stable equilibria to deterministic period k population cycles to Neimark-Sacker bifurcations and deterministic chaos. For these two models, we use an extension of the next generation matrix approach for calculating to account for populations with locally asymptotically stable period k cycles in the juvenile-adult disease-free system. When and the juvenile-adult demographic system (in the absence of the disease) has a locally asymptotically stable period k population cycle, we prove that the juvenile-adult disease goes extinct whenever . Under the same period k juvenile-adult demographic assumption but with , we prove that the juvenile-adult disease-free period k population cycle is unstable and the disease persists. When , our simulations show that the juvenile-adult disease-free period k cycle dynamics drives the juvenile-adult SIR disease dynamics, but not the juvenile-adult ISAv disease dynamics.

Keywords: juvenile adult; population; period; disease

Journal Title: Journal of Biological Dynamics
Year Published: 2020

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