Related papers: Parameter estimation for a hidden linear birth and…
This study aims to estimate the parameters of a stochastic exposed-infected epidemiological model for the transmission dynamics of notifiable infectious diseases, based on observations related to isolated cases counts only. We use the…
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
This study proposes a nonhomogeneous birth--death model which captures the dynamics of a directly transmitted infectious disease. Our model accounts for an important aspect of observed epidemic data in which only symptomatic infecteds are…
Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for…
The analysis of diffusion processes in real-world propagation scenarios often involves estimating variables that are not directly observed. These hidden variables include parental relationships, the strengths of connections between nodes,…
We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…
We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household…
In this paper, we consider a discrete-time stochastic SIR model, where the transmission rate and the true number of infectious individuals are random and unobservable. An advantage of this model is that it permits us to account for random…
Understanding the spread of COVID-19 has been the subject of numerous studies, highlighting the significance of reliable epidemic models. Here, we introduce a novel epidemic model using a latent Hawkes process with temporal covariates for…
Mathematical models of infectious disease transmission typically neglect within-host dynamics. Yet within-host dynamics - including pathogen replication, host immune responses, and interactions with microbiota - are crucial not only for…
We propose a new method for the estimation of parameters of hidden diffusion processes. Based on parametrization of the transition matrix, the Baum-Welch algorithm is improved. The algorithm is compared to the particle filter in application…
In this work, we aim to formalize a novel scientific machine learning framework to reconstruct the hidden dynamics of the transmission rate, whose inaccurate extrapolation can significantly impair the quality of the epidemic forecasts, by…
We consider immigration processes with binomial catastrophes and random survival parameters. Two sources of randomness are analyzed. In the first model, the survival parameter is independently resampled at each catastrophe. In the second…
Infectious diseases that incorporate pre-symptomatic transmission are challenging to monitor, model, predict and contain. We address this scenario by studying a variant of a stochastic susceptible-exposed-infected-recovered model on…
This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept…
Epidemic dynamics in a stochastic network of interacting epidemic centers is considered. The epidemic and migration processes are modelled by Markov's chains. Explicit formulas for probability distribution of the migration process are…
We study an immigration effect in the time-changed linear birth-death process where the immigration occurs only if the population goes extinct. We call this process as the time-fractional linear birth-death process with immigration…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…