Related papers: Epidemic branching processes with and without vacc…
Infectious diseases are still a major global burden for modern society causing 13 million deaths annually. One way to reduce the morbidity and mortality rates from infectious diseases is through preventative or targeted vaccinations.…
In this paper we consider a model based on branching process theory for the proliferation and the dissemination network of T cells in the adaptive immune response. A multi-type Galton Watson branching process is assumed as the basic…
We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
The propagation of model epidemics on a small-world network under the action of immunization is studied. Although the connectivity in this kind of networks is rather uniform, a vaccination strategy focused on the best connected individuals…
A mathematical model of COVID-19 with minimal compartments is developed. The model is simple enough to fit data on confirmed cases, estimate the hidden infection figure and incorporate the effect of vaccination. With the effect of the new…
Voluntary vaccination is effective to prevent infectious diseases from spreading. Both vaccination behavior and cognition of the vaccination risk play important roles in individual vaccination decision making. However, it is not clear how…
Vaccination campaigns have both direct and indirect effects that act to control an infectious disease as it spreads through a population. Indirect effects arise when vaccinated individuals block disease transmission in any infection chains…
In this work we consider a model of epidemic spreading coupled with an opinion dynamics in a fully-connected population. Regarding the opinion dynamics, the individuals may be in two distinct states, namely in favor or against a vaccination…
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.…
We show existence of a non-trivial phase transition for the contact process, a simple model for infection without immunity, on a network which reacts dynamically to the infection trying to prevent an epidemic. This network initially has the…
Our chances to halt epidemic outbreaks rely on how accurately we represent the population structure underlying the disease spread. When analyzing global epidemics this force us to consider metapopulation models taking into account intra-…
We model an epidemic where the per-person infectiousness in a network of geographic localities changes with the total number of active cases. This would happen as people adopt more stringent non-pharmaceutical precautions when the…
We study the phase transition between survival and extinction in an epidemic process with long-range interactions and immunization. This model can be viewed as the well-known general epidemic process (GEP) in which nearest-neighbor…
Consider a branching process $\{Z_n\}_{n\ge 0}$ with immigration in varying environment. For $a\in\{0,1,2,...\},$ let $C=\{n\ge0:Z_n=a\}$ be the collection of times at which the population size of the process attains level $a.$ We give a…
Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution…
We introduce a 2-layer network model for the study of the immunization dynamics in epidemics. Spreading of an epidemic is modeled as an excitatory process in a small-world network (body layer) while immunization by prevention for the…
Infectious pathogens often propagate by superspreading, which focusses onward transmission on disproportionately few infected individuals. At the same time, infector-infectee pairs tend to have more similar transmission potentials than…
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…