Related papers: The Poisson algorithm: a simple method to simulate…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
We investigate statistical inference across time scales. We take as toy model the estimation of the intensity of a discretely observed compound Poisson process with symmetric Bernoulli jumps. We have data at different time scales:…
Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a…
Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the…
Epidemiological compartmental models are useful for understanding infectious disease propagation and directing public health policy decisions. Calibration of these models is an important step in offering accurate forecasts of disease…
Many epidemic models are naturally defined as individual-based models: where we track the state of each individual within a susceptible population. Inference for individual-based models is challenging due to the high-dimensional state-space…
The emergence and spread of deadly pandemics has repeatedly occurred throughout history, causing widespread infections and loss of life. The rapid spread of pandemics have made governments across the world adopt a range of actions,…
Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails…
The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…
Statistical modeling of point patterns is an important and common problem in several areas. The Poisson process is the most common process used for this purpose, in particular, its generalization that considers the intensity function to be…
We present an algorithm for the problem of linear distributed estimation of a parameter in a network where a set of agents are successively taking measurements. The approach considers a roaming token in a network that carries the estimate,…
Several key metrics in public health convey the probability that a primary event will lead to a more serious secondary event in the future. These "severity rates" can change over the course of an epidemic in response to shifting conditions…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
The COVID-19 pandemic has been characterised by multiple waves of transmission driven by interventions and emerging variants, challenging epidemic models that assume gradually evolving transmission dynamics. We propose a class of…
We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the…
Emerging applications in engineering such as crowd-sourcing and (mis)information propagation involve a large population of heterogeneous users or agents in a complex network who strategically make dynamic decisions. In this work, we…
The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…
Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these…
Parameter inference and state estimation in stochastic and partially observed biological systems remain major problems in mathematical biology. In this work, we introduce a two-dimensional lattice graph model for the spread of infectious…
Obtaining accurate forecasts for the evolution of epidemic outbreaks from deterministic compartmental models represents a major theoretical challenge. Recently, it has been shown that these models typically exhibit trajectories' degeneracy,…