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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…
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,…
The basic reproduction number ($R_0$) is an epidemiological metric that represents the average number of new infections caused by a single infectious individual in a completely susceptible population. The methodology for calculating this…
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…
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…
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…
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 a threshold parameter for disease extinction or survival in isolated populations. However no human population is fully isolated from other human or animal populations. We use compartmental models to…
Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the R0 alternative"…
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.…
Branching processes are widely used to model evolutionary and population dynamics as well as the spread of infectious diseases. To characterize the dynamics of their growth or spread, the basic reproduction number $R_0$ has received…
The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation…
A reduction of a source distribution is a collection of smaller sized distributions that are collectively equivalent to the source distribution with respect to the property of decomposability. That is, an arbitrary language is decomposable…
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…
As widely known, the basic reproduction number plays a key role in weighing birth/infection and death/recovery processes in several models of population dynamics. In this general setting, its characterization as the spectral radius of next…
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…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
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 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…