Related papers: Asymptotic Behavior of SIRS Models in State-depend…
The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log-abundances of species, with…
In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…
Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to…
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically,…
In a collection of particles performing independent random walks on $\mathbb Z^d$ we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and…
This paper investigates the deterministic extinction and permanence of a family of SEIRS malaria models with multiple random delays, and with a general nonlinear incidence rate. The conditions for the extinction and permanence of the…
An SEIRS epidemic with disease fatalities is introduced in a growing population (modelled as a super-critical linear birth and death process). The study of the initial phase of the epidemic is stochastic, while the analysis of the major…
Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and…
Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the…
We simulate a spatial behavioral model of the diffusion of an infection to understand the role of geographic characteristics: the number and distribution of outbreaks, population size, density, and agents' movements. We show that several…
In a metapopulation network, infectious diseases spread widely because of the travel of individuals. In the present study, we consider a modified metapopulation Susceptible-Infected-Removed (SIR) model with a latent period, which we call…
This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral…
We study a class of SIRS epidemic dynamical models with a general non-linear incidence rate and transfer from infectious to susceptible. The incidence rate includes a wide range of monotonic, con- cave incidence rates and some non-monotonic…
We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent p-coin tosses. Spatial variants of these models are proposed, in which finite…
We explore the emergence of persistent infection in a closed region where the disease progression of the individuals is given by the SIRS model, with an individual becoming infected on contact with another infected individual within a given…
Self-adaptive dynamics occurs in many physical systems such as socio-economics, neuroscience, or biophysics. We formalize a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the…
Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
The annual occurrence of many infectious diseases remains a constant burden to public health systems. The seasonal patterns in respiratory disease incidence observed in temperate regions have been attributed to the impact of environmental…