Age structured discrete-time disease models with demographic population cycles

Area of Science:

• Mathematical Biology
• Epidemiology
• Ecology

Background:

• Age structure significantly impacts infectious disease dynamics.
• Population cycles can arise intrinsically from demographic processes.
• Understanding disease persistence requires integrating demographic and epidemiological models.

Purpose of the Study:

• To investigate how age structure and population cycles influence disease persistence and extinction.
• To analyze the basic reproduction number ([Formula: see text]) in juvenile-adult disease models.
• To compare disease dynamics in Susceptible-Infectious-Recovered (SIR) and Infectious-Salmon Anemia-Virus (ISA[Formula: see text]) models.

Main Methods:

• Utilized discrete-time juvenile-adult infectious disease models.
• Employed an extended next generation matrix approach to calculate [Formula: see text].
• Analyzed models with Beverton-Holt and Ricker recruitment functions, including period k cycles and chaotic dynamics.

Main Results:

• When [Formula: see text] and the disease-free system exhibits period k cycles, disease extinction occurs if [Formula: see text] < 1.
• Under period k cycles, disease persists if [Formula: see text] > 1, destabilizing the population cycle.
• Simulations show period k cycles drive SIR dynamics when [Formula: see text] > 1, but not ISA[Formula: see text] dynamics.

Conclusions:

• The interplay between demographic cycles and disease transmission is crucial for predicting disease outcomes.
• [Formula: see text] is a key threshold for disease persistence versus extinction in cyclically structured populations.
• Model-specific responses (SIR vs. ISA[Formula: see text]) highlight the importance of disease characteristics in age-structured populations.