Related papers: Exact and approximate analytic solutions in the SI…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
In this work, we revisit the basic reproduction rate $\mathcal{R}_{0}$ definition for analysis of epidemic-non-epidemic phases describing the dynamics of the discrete stochastic version of the epidemic $SIR$ model based on the Master…
In this paper we study a susceptible infectious recovered (SIR) model with asymptomatic patients, contact tracing and isolation on a configuration network. Using degree based approximation, we derive a system of differential equations for…
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…
An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in $\ln S$ and analytically continuing its divergent power series solution such that…
In contrast to the common assumption in epidemic models that the rate of infection between individuals is constant, in reality, an individual's viral load determines their infectiousness. We compare the average and individual reproductive…
In this work, the SIR epidemiological model is reformulated so to highlight the important {\em effective reproduction number}, as well as to account for the {\em generation time}, inverse of the {\em incidence rate}, and the {\em infectious…
The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The…
The ability to actually implement epidemic models is a crucial stake for public institutions, as they may be overtaken by the increasing complexity of current models and sometimes tend to revert to less elaborate models such as the SIR. In…
Variable individual response to epidemics may be found within many contexts in the study of infectious diseases (e.g., age structure or contact networks). There are situations where the variability, in terms of epidemiological parameter,…
We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and…
A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing…
This paper seeks to study the evolution of the COVID-19 pandemic based on daily published data from Worldometer website, using a time-dependent SIR model. Our findings indicate that this model fits well such data, for different chosen…
We study the extinction of epidemics in a generalized susceptible-infected-susceptible model, where a susceptible individual becomes infected with the rate $\lambda$ when contacting $m$ infective individual(s) simultaneously, and an…
Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by…
We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and…
We exhibit a scaling law for the critical SIS stochastic epidemic: If at time 0 the population consists of square root N infected and N - square root N susceptible individuals, then when time and number currently infected are both scaled by…
Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size $n$. A Markovian SIR (susceptible $\to$ infective $\to$ recovered) infectious disease,…
This paper studies the distribution function of the time of extinction of a subcritical epidemic, when a large enough proportion of the population has been immunized and/or the infectivity of the infectious individuals has been reduced, so…
In this work, we discuss the SIR epidemiological model and different variations of it applied to the propagation of the COVID-19 pandemia; we employ the data of the state of Guanajuato and of Mexico. We present some considerations that can…