Related papers: Epidemic branching processes with and without vacc…
Humans, domestic animals, orchard crops, and ornamental plants are commonly treated with antibiotics in response to bacterial infection. By curing infectious individuals, antibiotic therapy might limit the spread of contagious disease among…
Many pathogens spread primarily via direct contact between infected and susceptible hosts. Thus, the patterns of contacts or contact network of a population fundamentally shapes the course of epidemics. While there is a robust and growing…
In diseases with long-term immunity, vaccination is known to increase the average age at infection as a result of the decrease in the pathogen circulation. This implies that a vaccination campaign can have negative effects when a disease is…
We consider a vaccination game that results with the introduction of premature and possibly scarce vaccines introduced in a desperate bid to combat the otherwise ravaging deadly pandemic. The response of unsure agents amid many…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
In this study, we explore the dynamic interplay between the timing of vaccination campaigns and the trajectory of disease spread in a population. Through comprehensive data analysis and modeling, we have uncovered a counter-intuitive…
The aim of this paper is to introduce a multitype branching process with random migration following the research initiated with the Galton-Watson process with migration introduced in [Yanev & Mitov (1980) C. R. Acad. Bulg. Sci.…
With significant population fractions in many societies who refuse vaccines, it is important to reconsider how vaccination is incorporated into compartmental epidemiology models. It is still most common to apply the vaccination rate to the…
Humans, domestic animals, orchard crops, and ornamental plants are commonly treated with antibiotics in response to bacterial infection. By curing infectious individuals, antibiotic therapy might limit the spread of contagious disease among…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
Spreading processes represent a very efficient tool to investigate the structural properties of networks and the relative importance of their constituents, and have been widely used to this aim in static networks. Here we consider simple…
The mitigation of an infectious disease spreading has recently gained considerable attention from the research community. It may be obtained by adopting sanitary measurements social rules, together with an extensive vaccination campaign.…
Epidemics have shaped human history, often with devastating consequences, motivating the development of mathematical models to understand and control their dynamics. Among the many aspects of epidemic behavior, the conditions that lead to…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
By the end of 2020, a year since the first cases of infection by the Covid-19 virus have been reported, there is a light at the end of the tunnel. Several pharmaceutical companies made significant progress in developing effective vaccines…
The spread of infectious disease is strongly influenced by social dynamics. In addition to infection risk, individuals vaccination decisions depend on prevailing social behavior: high infection levels and widespread vaccination can increase…
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…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
We examine the population growth system called Q-processes. This is defined by the Galton-Watson Branching system conditioned on non-extinction of its trajectory in the remote future. In this paper we observe the total progeny up to time…
We consider the spread of a supercritical stochastic SIR (Susceptible, Infectious, Recovered) epidemic on a configuration model random graph. We mainly focus on the final stages of a large outbreak and provide limit results for the duration…