Related papers: An epidemic process mediated by a decaying diffusi…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
Models of biological processes are often subject to different sources of noise. Developing an understanding of the combined effects of different types of uncertainty is an open challenge. In this paper, we study a variant of the…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
Most previous studies of epidemic dynamics on complex networks suppose that the disease will eventually stabilize at either a disease-free state or an endemic one. In reality, however, some epidemics always exhibit sporadic and recurrent…
The contact process is a simple infection spreading model showcasing an out-of-equilibrium phase transition between a macroscopically active and an inactive phase. Such absorbing state phase transitions are often sensitive to the presence…
We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed by individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
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.…
The mechanism through which cells determine their fate is intimately related to the spreading of certain biochemical (so-called epigenetic) marks along their genome. The mechanisms behind mark spreading and maintenance are not yet fully…
Epidemic models often reflect characteristic features of infectious spreading processes by coupled non-linear differential equations considering different states of health (such as Susceptible, Infected, or Recovered). This compartmental…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that,…
We introduce the generalized diffusive epidemic process, which is a metapopulation model for an epidemic outbreak where a non-sedentary population of walkers can jump along lattice edges with diffusion rates $D_S$ or $D_I$ if they are…
Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load…
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…
Agent-based models of disease transmission involve stochastic rules that specify how a number of individuals would infect one another, recover or be removed from the population. Common yet stringent assumptions stipulate interchangeability…
The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the…
A class of stochastic vector-borne infectious disease models is derived and studied. The class type is determined by a general nonlinear incidence rate of the disease. The disease spreads in a highly random environment with variability from…
One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to…