R0 and Sensitivity Analysis of a Predator-Prey Model with Seasonality and Maturation Delay.

R0 and Sensitivity Analysis of a Predator-Prey Model with Seasonality and Maturation Delay. Math Biosci. 2019 Jul 05;:108225 Authors: Wang X, Wang H, Li MY Abstract Coexistence and seasonal fluctuations of predator and prey populations are common and well documented in ecology. Under what conditions can predators coexist with prey in a seasonally changing environment? What factors drive long-term population cycles of some predator and prey species? To answer these questions, we investigate an improved predator-prey model based on the Rosenzweig-MacArthur [1] model. Our model incorporates seasonality and a predator maturation delay, leading to a system of periodic differential equations with a time delay. We define the basic reproduction ratio R0 and show that it is a threshold parameter determining whether the predators can coexist with the prey. We show that if R0 < 1, then the prey population has seasonal variations and the predator population goes extinct. If R0 > 1, then the prey and the predators coexist and fluctuate seasonally. As an example, we study a Daphnia-algae system and explore possible mechanisms for seasonal population cycles. Our numerical simulations indicate that seasonal Daphnia-algae cycles are attributed to seasonality rather than Daphnia maturation delay or Daphnia-algae interaction. The Daphnia maturation delay, the amplitude of algae growth rate and the amplitude of the carrying capacity are fo...
Source: Mathematical Biosciences - Category: Statistics Authors: Tags: Math Biosci Source Type: research