Effects of Seasonal Births and Predation on Disease Spread

For many organisms, births occur in seasonal pulses. When predation on an organism is density-dependent, seasonal population changes also change the per capita predation rate. This in turn can affect disease dynamics in the system. We use a Susceptible-Infected (SI) model to study the effects of seasonal births and nonlinear predation on the spread of infection in a population over time. Motivated by open marine systems, we assume that the total birth or recruitment rate is density-independent and that the predator population is constant. We compare models with constant year-round births and seasonally pulsed births as well as linear and hyperbolic predation functions. We calculate the basic reproductive number and use numerical simulations to examine system behavior when infection is endemic. When predation depends linearly on prey populations, seasonality of births does not affect the average infection level or disease transmissibility. When predation rates saturate, as in systems with hyperbolic predation, higher disease transmissibility and endemic infection levels result. This effect can be exacerbated by seasonality of births, especially at moderate population levels.