Related papers: Birth/birth-death processes and their computable t…
In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier…
Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular…
Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown…
We present a perfect simulation algorithm for measures that are absolutely continuous with respect to some Poisson process and can be obtained as invariant measures of birth-and-death processes. Examples include area- and…
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel…
We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…
The dynamics of fractional population sizes y_i=Y_i/N in homogeneous compartment models with time dependent total population N is analyzed. Assuming constant per capita birth and death rates the vector field Y_i'=V_i(Y) naturally projects…
Ageing's sensitivity to natural selection has long been discussed because of its apparent negative effect on individual's fitness. Thanks to the recently described (Smurf) 2-phase model of ageing we were allowed to propose a fresh angle for…
Sampling a probability distribution with known likelihood is a fundamental task in computational science and engineering. Aiming at multimodality, we propose a new sampling method that takes advantage of both birth-death process and…
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
Approximate Bayesian computation (ABC) methods can be used to sample from posterior distributions when the likelihood function is unavailable or intractable, as is often the case in biological systems. ABC methods suffer from inefficient…
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
Using an extended version of the credit risk model CreditRisk+, we develop a flexible framework with numerous applications amongst which we find stochastic mortality modelling, forecasting of death causes as well as profit and loss…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…
A one-to-one correspondence is established between the bridge path space of birth-death processes and the exclusive union of the product spaces of simplexes and integer grids. Formulae are derived for the exact counting of the integer grid…
Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the…
We propose the following model for speciation and extinction. Birth and deaths occur according to spatially inhomogeneous contact rates. We assume that the ratio of the birth rate over the death rate at a site converges to some limit as the…
Different ways of calculating mortality ratios during epidemics have yielded very different results, particularly during the current COVID-19 pandemic. We formulate both a survival probability model and an associated infection…
In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying It\^o's calculus and the trend functions of the proposed process is calculated. The…