Related papers: Epidemic branching processes with and without vacc…
The success of a vaccination program is crucially dependent on its adoption by a critical fraction of the population, as the resulting herd immunity prevents future outbreaks of an epidemic. However, the effectiveness of a campaign can…
This work describes a simple agent model for the spread of an epidemic outburst, with special emphasis on mobility and geographical considerations, which we characterize via statistical mechanics and numerical simulations. As the mobility…
Opposition to vaccination has long been a non-negligible public health phenomenon resulted from people's varied perceptions toward vaccination (e.g., vaccine-phobia). This paper investigates the voluntary vaccination behavior of a…
Motivated by the study of a parasite infection in a cell line, we introduce a general class of Markov processes for the modelling of population dynamics. The population process evolves as a diffusion with positive jumps whose rate is a…
This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a…
We study the iterated Galton-Watson process (IGW), possibly with thinning, introduced by Gawe{\l}and Kimmel to model the number of repeats of DNA triplets during some genetic disorders. If the process involves some thinning, then extinction…
Branching processes model the evolution of populations of agents that randomly generate offsprings. These processes, more patently Galton-Watson processes, are widely used to model biological, social, cognitive, and technological phenomena,…
We analyze infection spreading processes in a system where only a fraction $p$ of individuals can be affected by disease, while remaining $1-p$ individuals are immune. Such a picture can emerge as a natural consequence of previously…
This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments…
The introduction of the rotavirus vaccine in the United Kingdom (UK) in 2013 led to a noticeable decline in laboratory reports in subsequent years. To assess the impact of vaccination on rotavirus transmissibility we calibrated a stochastic…
We study a susceptible-vaccinated--infected--recovered (SVIR) epidemic-spreading model with diversity of infection rate of the individuals. By means of analytical arguments as well as extensive computer simulations, we demonstrate that the…
We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence…
The decision of whether or not to vaccinate is a complex one. It involves the contribution both to a social good -- herd immunity -- and to one's own well being. It is informed by social influence, personal experience, education, and mass…
Vaccines not only directly protect vaccinated individuals but also contribute to protect the entire population via indirect herd-immunity benefits. However, researchers have long struggled to quantify these indirect effects at the…
In order to meet regulatory approval, pharmaceutical companies often must demonstrate that new vaccines reduce the total risk of a post-infection outcome like transmission, symptomatic disease, severe illness, or death in randomized,…
We analyse a stochastic SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of…
The containment of epidemic spreading is a major challenge in science. Vaccination, whenever available, is the best way to prevent the spreading, because it eventually immunizes individuals. However, vaccines are not perfect, and total…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
We study the evolution of the population size distribution of a critical Galton-Watson process with infinite variance of the offspring size of particles assuming that the population size is unusually small at the distant moment $n$ of…
Branching processes $(Z_n)_{n \ge 0}$ in a varying environment generalize the Galton-Watson process, in that they allow time-dependence of the offspring distribution. Our main results concern general criteria for a.s. extinction,…