Related papers: Parameter estimation for a hidden linear birth and…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
Infectious disease outbreaks have precipitated a profusion of mathematical models. Epidemic curves predicted by these models are typically qualitatively similar, despite distinct model assumptions, but there is no theoretical explanation…
The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…
Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…
We introduce a modified spatial $\Lambda$-Fleming-Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective…
Consider the following birth and death process with the following infinitesimal transition probabilities {\lambda}(k) ={\lambda}/(1+k) and {\mu}(k) = {\mu}k with {\lambda},{\mu}> 0. This process has known as a discouragement queue [5].…
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global…
In many cases, tainted information in a computer network can spread in a way similar to an epidemics in the human world. On the other had, information processing paths are often redundant, so a single infection occurrence can be easily…
Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility ($\sigma_{inh}$) and external infectivity ($\iota_{ext}$), in a given population.…
When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based…
First Few X (FFX) studies collect household-stratified data in the early stages of a pandemic, in order to infer severity and transmissibility of an emerging disease. We present a Bayesian method to approximately infer population-level…
The time-to-recovery or time-to-death for various infectious diseases can vary significantly among individuals, influenced by several factors such as demographic differences, immune strength, medical history, age, pre-existing conditions,…
In this paper, we develop a method to estimate the infection-rate of a disease, over a region, as a field that varies in space and time. To do so, we use time-series of case-counts of symptomatic patients as observed in the areal units that…
The epidemic threshold of a spreading process indicates the condition for the occurrence of the wide spreading regime, thus representing a predictor of the network vulnerability to the epidemic. Such threshold depends on the natural history…
Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using…
In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described.…
Cure rate models are mostly used to study data arising from cancer clinical trials. Its use in the context of infectious diseases has not been explored well. In 2008, Tournoud and Ecochard first proposed a mechanistic formulation of cure…
The paper contains the complete analysis of the Galton-Watson models with immigration, including the processes in the random environment, stationary or non-stationary ones. We also study the branching random walk on $Z^d$ with immigration…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
We study metapopulation models for the spread of epidemics in which different subpopulations (cities) are connected by fluxes of individuals (travelers). This framework allows to describe the spread of a disease on a large scale and we…