The mean operator R0 and its dual R0 play an important role and have many applications, for example, in image processing of the so-called synthetic aperture radar (SAR) data [11, 12] or in the linearized inverse scattering problem in acoustics [6]. Our purpose in this work is to define and study integral transforms which generalize the operators R0 and R0. More precisely, we consider the follow...

We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. The model admits a unique endemic equilibrium if and only if the basic reproduction number R0 exceeds one, while the trivial equilibrium and the disease-free equilibrium a...

We study the global stability of a human immunodeficiency virus (HIV) infection model with Cytotoxic T Lymphocytes (CTL) immune response. The model describes the interaction of the HIV with two classes of target cells, CD4(+) T cells and macrophages. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replicatio...

We compare threshold results for the deterministic and stochastic versions of the homogeneous SI model with recruitment, death due to the disease, a background death rate, and transmission rate beta cXY/N. If an infective is introduced into a population of susceptibles, the basic reproduction number, R0, plays a fundamental role for both, though the threshold results differ somewhat. For the de...

The basic reproductive ratio, R0, is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. Most importantly, R0 often serves as a threshold parameter that predicts whether an infection will spre...

Doubled haploids of carnation (Dianthus caryophyllus L.) were obtained by pseudofertilized ovule culture. Emasculated ̄ower buds of carnation were pollinated with pollen inactivated by Xray irradiation. After 2±3 weeks, the ovaries were explanted and were cultured on solid MS medium containing 2 mM NAA, 2 mM BAP and 6% sucrose. Regenerated plants(R0) were morphologically different from the moth...

An epidemic model with incomplete treatment and vaccination for the newborns and susceptibles is constructed. We establish that the global dynamics are completely determined by the basic reproduction number R0. If R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. If R0 > 1, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also ...

The basic reproduction number, R0 is a measure of the potential for disease spread in a population. Mathematically, R0 is a threshold for stability of a disease-free equilibrium and is related to the peak and final size of an epidemic. The purpose of these notes is to give a precise definition and algorithm for obtaining R0 for a general compartmental ordinary differential equation model of dis...

In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number R0 of the model is obtained. We investigate the global behavior of the model in terms of R0: if R0 ≤ 1, then the infection-free equilibrium is globally asymptotically stable, whereas if R0 > 1, then the infection equilibrium is global...

By incorporating an additional recovery compartment in the SLBS model, a new model, known as the SLBRS model, is proposed in this paper. The qualitative properties of this model are investigated. The result shows that the dynamic behavior of the model is determined by a threshold R0. Specially, virus-free equilibrium is globally asymptotically stable if R0 ≤ 1, whereas the viral equilibrium is ...