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We introduce the Hawkes process with renewal immigration and make its statistical estimation possible with two Expectation Maximization (EM) algorithms. The standard Hawkes process introduces immigrant points via a Poisson process, and each…
For estimating area-specific parameters (quantities) in a finite population, a mixed model prediction approach is attractive. However, this approach strongly depends on the normality assumption of the response values although we often…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
Stochastic compartmental models are important tools for understanding the course of infectious diseases epidemics in populations and in prospective evaluation of intervention policies. However, calculating the likelihood for discretely…
We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain…
We study the random times between successive cases in a transmission chain of infectious diseases with asymptomatic carriers. We derive the probability distribution of this generation time (in days) from a discrete-time epidemic model with…
We reformulate models in epidemiology and population dynamics in terms of probability distributions. This allows us to construct the Fisher information, which we interpret as the metric of a one-dimensional differentiable manifold. For…
Individual-level epidemic models are increasingly being used to help understand the transmission dynamics of various infectious diseases. However, fitting such models to individual-level epidemic data is challenging, as we often only know…
A novel predictive modeling framework for the spread of infectious diseases using high dimensional partial differential equations is developed and implemented. A scalar function representing the infected population is defined on a…
Stochastic state-transition models of infectious disease transmission can be used to deduce relevant drivers of transmission when fitted to data using statistically principled methods. Fitting this individual-level data requires inference…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact…
In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…
Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious disease epidemics are compartmental models. They stratify…
Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…
In medical research, understanding changes in outcome measurements is crucial for inferring shifts in health conditions. However, traditional methods often struggle with large, irregularly longitudinal data and fail to account for the…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…
Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…
The effective reproduction number is an important descriptor of an infectious disease epidemic. In small populations, ideally we would estimate the effective reproduction number using a Markov Jump Process (MJP) model of the spread of…
In Section 1, we revisit the partial differential equation (PDE) for the probability generating function (PGF) of the time-nonhomogeneous BDI (birth-and-death-with-immigration) process and derive a closed form solution. To the best of our…