Related papers: Moderate deviations and extinction of an epidemic
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…
We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a…
We introduce and study a model stemming from game theory for the spread of an epidemic throughout a given population. Each agent is allowed to choose an action whose value dictates to what extent they limit their social interactions, if at…
In this work, we study the critical behavior of an epidemic propagation model that considers individuals that can develop drug resistance. In our lattice model, each site can be found in one of four states: empty, healthy, normally infected…
We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations…
Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts…
In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global…
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…
A model for large-scale evolution recently introduced by Amaral and Meyer is studied analytically and numerically. Species are located at different trophic levels and become extinct if their prey becomes extinct. It is proved that this…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…
Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
We study the Susceptible-Infected-Susceptible model of the spread of an endemic infection. We calculate an exact expression for the mean number of transmissions for all values of the population and the infectivity. We derive the large-N…
A stochastic SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a social network is analysed. The underlying social network is described by an Erd\H{o}s-R\'{e}nyi random graph but, during the course of the epidemic,…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…
This paper combines a canonical epidemiology model of disease dynamics with government policy of lockdown and testing, and agents' decision to social distance in order to avoid getting infected. The model is calibrated with data on deaths…