Related papers: The Basic Reproduction Number for Petri Net Models…
Accurate epidemic forecasting requires models that account for the layered and heterogeneous nature of real social interactions. The basic reproduction number $\mathcal R_0$ calculated from models that assume homogeneous mixing or…
This work provides a geometric version of the next-generation matrix method for obtaining the basic reproduction number of an epidemiological model. We exhibit a certain correspondence between any system of ODEs and Petri nets. We observe…
In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, $R_0$, for Markovian epidemics in structured populations. The methodology derived is applicable…
Epidemic models are a valuable tool in the decision making process. Once a mathematical model for an epidemics has been established, the very next step is calculating a mathematical expression for the basic reproductive number, $R_0$, which…
The basic reproduction number, $R_0$ is an important and widely used concept in the study of infectious diseases. We briefly review the recent trend of calculating the average of various $R_0$ estimates in systematic reviews aimed at…
The basic reproductive number -- $R_0$ -- is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that…
The basic reproduction number R0 -- the number of individuals directly infected by an infectious person in an otherwise susceptible population -- is arguably the most widely used estimator of how severe an epidemic outbreak can be. This…
We propose a novel approach to approximate the basic reproduction number $R_0$ as spectral radius of the Next-Generation Operator in time-periodic population models by characterizing the latter via evolution semigroups. Once birth/infection…
In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number $R_0$ and show that $R_0$ is a threshold parameter: if $R_0\le 1$ the disease free steady state is globally stable; if $R_0>1$…
For a heterogeneous host population, the basic reproduction number of an infectious disease, $\cR_0$, is defined as the spectral radius of the next generation operator (NGO). The threshold properties of the basic reproduction number are…
In this paper we consider epidemic models of directly transmissible SIR (susceptible $\to$ infective $\to$ recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting…
An important issue in theoretical epidemiology is the epidemic threshold phenomenon, which specify the conditions for an epidemic to grow or die out. In standard (mean-field-like) compartmental models the concept of the basic reproductive…
The basic reproduction number $R_0$ is a fundamental quantity in epidemiological modeling, reflecting the typical number of secondary infections that arise from a single infected individual. While $R_0$ is widely known to scientists,…
A key parameter in models for the spread of infectious diseases is the basic reproduction number $R_0$, which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly…
In the framework of population dynamics, the basic reproduction number R_0 is, by definition, the expected number of offspring that an individual has during its lifetime. In constant and time periodic environments it is calculated as the…
A basic reproduction number, $R_0$, is a concept encountered frequently in the study of ecological and epidemiological models. It is routinely used to determine the stability of an extinction or a disease-free fixed point or steady state.…
When an infectious disease strikes a population, the number of newly reported cases is often the only available information that one can obtain during early stages of the outbreak. An important goal of early outbreak analysis is to obtain a…
In the face of an infectious disease, a key epidemiological measure is the basic reproduction number, which quantifies the average secondary infections caused by a single case in a susceptible population. In practice, the effective…
Reproduction numbers, like the basic reproduction number $\mathcal{R}_0$, play an important role in the analysis and application of dynamic models, including contagion models and ecological population models. One difficulty in deriving…
When controlling an emerging outbreak of an infectious disease it is essential to know the key epidemiological parameters, such as the basic reproduction number $R_0$ and the control effort required to prevent a large outbreak. These…