Related papers: Asymptotic Behavior of SIRS Models in State-depend…
The persistence exponent, which characterises the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining…
The spreading of an infectious disease can trigger human behavior responses to the disease, which in turn plays a crucial role on the spreading of epidemic. In this study, to illustrate the impacts of the human behavioral responses, a new…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating…
We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
We analyze the susceptible-infected-susceptible model for epidemic spreading in which a fraction of the individuals become immune by vaccination. This process is understood as a dilution by vaccination, which decreases the fraction of the…
Transmission rates in epidemic outbreaks may vary over time depending on the societal response. Non-pharmacological mitigation strategies such as social distancing and the adoption of protective equipment aim precisely at reducing…
We propose an epidemic compartment model, which includes mortality caused by the disease, but excludes demographic birth and death processes. Individuals are represented by random walkers, which are in one of the following states…
We study the spread of stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school…
In this paper, we study a single-species population model with pulse toxicant input to a small polluted environment. The intrinsic rate of population is affected by environment and toxin in organisms. The toxin in organisms is influenced by…
This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We…
A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing…
We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
The spread of an epidemic process is considered in the context of a spatial SIR stochastic model that includes a parameter $0\le p\le 1$ that assigns weights $p$ and $1- p$ to global and local infective contacts respectively. The model was…
We consider an epidemiological model that includes waning and boosting of immunity. Assuming that repeated exposure to the pathogen fully restores immunity, we derive an SIRS-type model with discrete and distributed delays. First we prove…
We consider a random walk with death in $[-N,N]$ moving in a time dependent environment. The environment is a system of particles which describes a current flux from $N$ to $-N$. Its evolution is influenced by the presence of the random…
The last decade saw the advent of increasingly realistic epidemic models that leverage on the availability of highly detailed census and human mobility data. Data-driven models aim at a granularity down to the level of households or single…
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological…