Related papers: The Basic Reproduction Number for Petri Net Models…
The effective reproduction number, R(t), is a central point in the study of infectious diseases. It establishes in an explicit way the extent of an epidemic spread process in a population. The current estimation methods for the time…
For nearly a century, the initial reproduction number (R0) has been used as a one number summary to compare outbreaks of infectious disease, yet there is no `standard' estimator for R0. Difficulties in estimating R0 arise both from how a…
In the real world, many complex systems interact with other systems. In addition, the intra- or inter-systems for the spread of information about infectious diseases and the transmission of infectious diseases are often not random, but with…
Early in an infectious disease outbreak, timely and accurate estimation of the basic reproduction number ($R_0$) and the serial interval (SI) is critical for understanding transmission dynamics and informing public health responses. While…
An approach to estimate the influence of the treatment-type controls on the basic reproduction number, R 0 , is proposed and elaborated. The presented approach allows one to estimate the effect of a given treatment strategy or to compare a…
Plant diseases often cause serious yield losses in agriculture. A pathogen's reproductive fitness can be quantified by the basic reproductive number, R0. Since pathogen transmission between host plants depends on the spatial separation…
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…
A pulse vaccination SIR model with periodic infection rate $\beta (t)$ have been proposed and studied. The basic reproductive number $R_0$ is defined. The dynamical behaviors of the model are analyzed with the help of persistence,…
We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge…
Real epidemic spreading networks often composed of several kinds of networks interconnected with each other, and the interrelated networks have the different topologies and epidemic dynamics. Moreover, most human diseases are derived from…
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 great issue of discussion of an infectious disease is its basic reproduction number R0, which provides an estimation of the contagiousness of the disease. When R0 > 1, the disease spread will potentially lead to an outbreak, such that of…
During infectious disease outbreaks, estimates of time-varying pathogen transmissibility, such as the instantaneous reproduction number R(t) or epidemic growth rate r(t), are used to inform decision-making by public health authorities. For…
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…
We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate and it is shown the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence.…
We study a multitype SIR epidemic model where individuals are categorized into different types, and where infection spread is characterized by a next-generation matrix $M=\{m_{ij}\}$ with community fractions $\{\pi_j\}$ for the different…
We develop a multi-patch and multi-group model that captures the dynamics of an infectious disease when the host is structured into an arbitrary number of groups and interacts into an arbitrary number of patches where the infection takes…
Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose a SEIRE epidemic model to describe the spread of the…
A general stochastic model for susceptible -> infective -> recovered (SIR) epidemics in non homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…