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We study the stochastic spatial Lotka-Volterra model for predator-prey interaction subject to a periodically varying carrying capacity. The Lotka-Volterra model with on-site lattice occupation restrictions (i.e., finite local carrying capacity) that represent finite food resources for the prey population exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by the existence of spatio-temporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis in order to specifically delineate the impact of stochastic fluctuations and spatial correlations. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The (quasi-)stationary regime of our periodically varying Lotka-Volterra predator-prey system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity-switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semi-quantitative description of the (quasi-)stationary state. 

We apply a perturbative Doi-Peliti field-theoretical analysis to the stochastic spatially extended symmetric Rock-paper-Scissors (RPS) and May-Leonard (ML) models, in which three species compete cyclically. Compared to the two-species Lotka-Volterra predator-prey (LV) model, according to numerical simulations, these cyclical models appear to be less affected by intrinsic stochastic fluctuations. Indeed, we demonstrate that the qualitative features of the ML model are insensitive to intrinsic reaction noise. In contrast, and although not yet observed in numerical simulations, we find that the RPS model acquires significant fluctuation-induced renormalizations in the perturbative regime, similar to the LV model. We also study the formation of spatio-temporal structures in the framework of stability analysis and provide a clearcut explanation for the absence of spatial patterns in the RPS system, whereas the spontaneous emergence of spatio-temporal structures features prominently in the LV and the ML models. 

Abstract We employ individual-based Monte Carlo computer simulations of a stochastic SEIR model variant on a two-dimensional Newman–Watts small-world network to investigate the control of epidemic outbreaks through periodic testing and isolation of infectious individuals, and subsequent quarantine of their immediate contacts. Using disease parameters informed by the COVID-19 pandemic, we investigate the effects of various crucial mitigation features on the epidemic spreading: fraction of the infectious population that is identifiable through the tests; testing frequency; time delay between testing and isolation of positively tested individuals; and the further time delay until quarantining their contacts as well as the quarantine duration. We thus determine the required ranges for these intervention parameters to yield effective control of the disease through both considerable delaying the epidemic peak and massively reducing the total number of sustained infections.