相关论文: Hamiltonian analysis of subcritical stochastic epi…

We consider stochastic population processes that are almost surely absorbed at the origin within finite time. Our interest is in the quasistationary distribution, $\boldsymbol{u}$, and the expected time, $\tau$, from quasistationarity to…

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no…

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…

In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…

We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective…

The Hamiltonian Mean-Field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived,…

Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a…

Errors of approximations of the quasi-stationary distribution (the QSD) of the logistic SIS model are evaluated numerically. The results are used to derive asymptotic approximations of the approximation errors for large populations. We show…

Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and…

Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that enlarge a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the…

Stochastic effects may cause fade-out of an infectious disease in a population immediately after an epidemic outbreak. We develop WKB theory to determine the most probable path of the system toward epidemic fade-out and to evaluate the…

We calculate both the exponential and pre-factor contributions in a WKB approximation of the master equation for a stochastic SIR model with highly oscillatory dynamics. Fixing the basic parameters of the model we investigate how the…

Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…

Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially…

This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…

This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…

We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on…

Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…

The acute phase of the Covid-19 pandemic has made apparent the need for decision support based upon accurate epidemic modeling. This process is substantially hampered by under-reporting of cases and related data incompleteness issues. In…

We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the…