Related papers: Outbreak size distributions in epidemics with mult…
We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household…
This work is concerned with epidemiological models defined on networks, which highlight the prominent role of the social contact network of a given population in the spread of infectious diseases. In particular, we address the modelling and…
In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR…
Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by time series of daily infections plateauing over extended periods of time. We prove that such…
Models for resident infectious diseases, like the SIRS model, may settle into an endemic state with constant numbers of susceptible ($S$), infected ($I$) and recovered ($R$) individuals, where recovered individuals attain a temporary…
Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the…
Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the…
Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved.…
We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions…
During the COVID pandemic, periods of exponential growth of the disease have been mitigated by containment measures that in different occasions have resulted in a power-law growth of the number of cases. The first observation of such…
Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network…
An ultrametric model of epidemic spread of infections based on the classical SIR model is proposed. Ultrametrics on a set of individuals based on theire hierarchical clustering relativly to the average time of infectious contact is…
We develop a multiple compartment Susceptible-Infected-Recovered (SIR) model to analyze the spread of several infectious diseases through different geographic areas. Additionally, we propose a data-quality sensitive optimization framework…
Metapopulation epidemic models describe epidemic dynamics in networks of spatially distant patches connected with pathways for migration of individuals. In the present study, we deal with a susceptible-infected-recovered (SIR)…
The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals' viral load in the disease transmission by proposing a new…
The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…
Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling…
It has been known that epidemic outbreaks in the SIR model on networks are described by phase transitions. Despite the similarity with percolation transitions, whether an epidemic outbreak occurs or not cannot be predicted with probability…
We introduce a modified SIR model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states susceptible (${\bf S}$), infected (${\bf I}$) or recovered (${\bf R}$). In…
Epidemics unfold by means of a spreading process from each infected individual to a random number of secondary cases. It has been claimed that the so-called superspreading events in COVID-19 are governed by a power-law tailed distribution…