Related papers: Delay compartment models from a stochastic process
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions,…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are…
Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
Spatio-temporal hidden Markov models are extremely difficult to estimate because their latent joint distributions are available only in trivial cases. In the estimation phase, these latent distributions are usually substituted with…
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…
In this paper, a brief review of delay population models and their applications in ecology is provided. The inclusion of diffusion and nonlocality terms in delay models has given more capabilities to these models enabling them to capture…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
By convention, and even more often, as an unintentional consequence of design, time distributions of latency and infectious durations in stochastic epidemic simulations are often exponential. The skewed distribtion typically leads to…
Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system…
The primary goal of this research is to investigate the impact of delay on the dynamics of the Susceptible-Exposed-Infected-Recovered-Death and Susceptible (SEIRDS) model, to which we add a stochastic term to account for uncertainty in…
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
In this paper we present a new method for deriving It\^{o} stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME,…
Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity…
We investigate the application of a framework for sparse model identification of differential equations from timeseries data in the context of compartmental models in epidemiology. Such frameworks often seek a sparse representation from a…
Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…