Related papers: Stochastic Fluctuations in Epidemics on Networks
The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that…
We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behaviour in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…
The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic SIR (Susceptible-Infective-Recovered) model on complex networks. It was found that in addition to the reduction of the effective…
Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be…
Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions,…
Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system…
It is well known that behavioral changes in contact patterns may significantly affect the spread of an epidemic outbreak. Here we focus on simple endemic models for recurrent epidemics, by modelling the social contact rate as a function of…
We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear. randomly. Using a constructive transition approach that predicts large outbreaks, prior to their occurrence, we derive an adaptive control.…
Changes in human behavior are increasingly recognized as a major determinant of epidemic dynamics. Although collective activity can be modified through imposed measures to control epidemic progression, spontaneous changes can also arise as…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can…
This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number $\mathscr{R}_0$…
Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localised clusters, suggesting a simple mechanism…
Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's…
Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, including stochastic and coherence resonance, noise induced bistability, noise-induced oscillations, to name but a few. In this paper we revisit a mechanism…
The abundance of a species' population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…