Related papers: Epidemic branching processes with and without vacc…
Consider a population evolving as a discrete-time supercritical multi-type Galton--Watson process. Suppose we run the process for $T$ generations, then sample $k$ individuals uniformly at generation $T$ and trace their genealogy backwards…
The shape of an epidemic wave in simple epidemic models applies to a homogeneous distribution of infected people in the population. In large inhomogeneous systems, at country-scale for instance, the wave shape is similar except for the…
This study aims to statistically assess the effectiveness of vaccination against SARS-CoV-2. It is indispensable to investigate the relationship between Covid-19 deadliness and vaccination in order to study the impact of vaccine in…
We introduce and study a model stemming from game theory for the spread of an epidemic throughout a given population. Each agent is allowed to choose an action whose value dictates to what extent they limit their social interactions, if at…
We study equilibrium distancing during epidemics. Distancing reduces the individual's probability of getting infected but comes at a cost. It creates a single-peaked epidemic, flattens the curve and decreases the size of the epidemic. We…
The COVID-19 vaccine reduces infection risk: even if one contracts COVID-19, the probability of complications like death or hospitalization is lower. However, vaccination may prompt people to decrease preventive behaviors, such as staying…
Optimal strategies for epidemic containment are focused on dismantling the contact network through effective immunization with minimal costs. However, network fragmentation is seldom accessible in practice and may present extreme side…
This paper is concerned with an extended Galton-Watson process so as to allow individuals to live and reproduce for more than one unit time. We assume that each individual can live $k$ seasons (time-units) with probability $h_k$, and…
The impact of information dissemination on epidemic control is essentially subject to individual behaviors. Unlike information-driven behaviors, vaccination is determined by many cost-related factors, whose correlation with the information…
This paper uses new and existing methods to study collective trends across countries throughout the pandemic, with a focus on the multivariate time series of reproduction numbers and vaccine proliferation. We begin with a time-varying…
We present a differential equations model in which contagious disease transmission is affected by contagious fear of the disease and contagious fear of the control, in this case vaccine. The three contagions are coupled. The two fears…
We consider a multi-type Galton-Watson branching processes, where the largest in magnitude positive eigenvalue $\rho$ of the first moments matrix is close to unity. Specifically, we examine the random vector representing the number of…
The dynamics of strongly immunizing childhood infections is still not well understood. Although reports of successful modeling of several incidence data records can be found in the literature, the key determinants of the observed temporal…
We investigate the distribution of numbers of secondary cases in households in the Office for National Statistics COVID-19 Infection Survey (ONS CIS), stratified by timing of vaccination and infection in the households. This shows a total…
Vaccination and outbreak monitoring are essential tools for preventing and minimizing outbreaks of infectious diseases. Targeted strategies, where the individuals most important for monitoring or preventing outbreaks are selected for…
We prove a scaling limit theorem for two-type Galton-Waston branching processes with interaction. The limit theorem gives rise to a class of mixed state branching processes with interaction using to simulate the evolution for cell division…
A cholera transmission model incorporating water-borne and horizontal transmissions as well as infectivity of deceased individuals is formulated and studied. The model also describes an imperfect and waning vaccination. Global stability of…
By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of…
We use analytical methods to investigate a continuous vaccination strategy effects on the infectious disease dynamics in a closed population and a demographically open population. The methodology and key assumptions are based on Breda et al…
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…