Related papers: Stochastic epidemics in a homogeneous community
We extend our BDI (birth-death-immigration) process based stochastic model of an infectious disease to time-nonhomogeneous cases. First, we discuss the deterministic model, and derive the expected value of the infection process. Then as an…
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…
We consider an individual-based SIR stochastic epidemic model in continuous space. The evolution of the epidemic involves the rates of infection and cure of individuals. We assume that individuals move randomly on the two-dimensional torus…
Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible $S$, infected $I$, removed $R$ and dead people $D$. In order to have…
Human mobility, contact patterns, and their interplay are key aspects of our social behavior that shape the spread of infectious diseases across different regions. In the light of new evidence and data sets about these two elements,…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…
We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barab\'asi-Albert (BA),…
Deterministic compartmental models have been used extensively in modeling epidemic propagation. These models are required to fit available data and numerical procedures are often implemented to this end. But not every model architecture is…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
Classical compartmental models in epidemiology often assume a homogeneous population for simplicity, which neglects the inherent heterogeneity among individuals. This assumption frequently leads to inaccurate predictions when applied to…
Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time…
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state…
A stochastic SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a social network is analysed. The underlying social network is described by an Erd\H{o}s-R\'{e}nyi random graph but, during the course of the epidemic,…
We consider a threshold epidemic model on a clustered random graph with overlapping communities. In other words, our epidemic model is such that an individual becomes infected as soon as the proportion of her infected neighbors exceeds the…
We study the spread of stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
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…
We introduce an epidemic model with varying infectivity and general exposed and infectious periods, where the infectivity of each individual is a random function of the elapsed time since infection, those function being i.i.d. for the…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…