In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproducti...

AIM The objective of this study was the investigation of a possible improvement of tumor resection rate, i.e. R0 vs. R1 resection when intraoperative ultrasound evaluation of tissue margins is used during breast-conserving surgery (BCS). PATIENTS AND METHODS A total of 250 cases were evaluated retrospectively. The impact of ultrasound analysis onto clean margin rates was evaluated. A subgroup...

In this paper, we first propose a time-periodic reaction–diffusion epidemic model which incorporates simple demographic structure and the latent period of infectious disease. Then we introduce the basic reproduction number R0 for this model and prove that the sign of R0 − 1 determines the local stability of the disease-free periodic solution. By using the comparison arguments and persistence th...

Clustering of cosmic-ray sources a†ects the Ñux observed beyond the cuto† imposed by the cosmic microwave background and may be important in interpreting the AGASA, FlyÏs Eye, and HiRes data. The standard deviation, p, in the predicted number N of events above 1020 eV is p/N \ 0.9(r0/10 Mpc)0.9, where is the unknown scale length of the correlation function Mpc for Ðeld galaxies, r0 (r0^ 10 km s...

We consider a real Gaussian process X with unknown smoothness r0 ∈ N0 where the mean-square derivative X(r0) is supposed to be Hölder continuous in quadratic mean. First from selected sampled observations, we study reconstruction of X(t), t ∈ [0, 1] with X̃r(t), a piecewise polynomial interpolation of degree r ≥ 1. We show that the mean-square error of the interpolation is a decreasing function ...

Using a multiple stage age of infection model, we derive an expression for the basic reproduction number, R0. We apply this method to find R0 in analogous treatment models. We find, in the model without treatment, R0 depends only on the mean infective period, and not on the infective distribution. In treatment models, R0 depends on the mean infective and mean treatment period, as well as the di...

We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in transmission patterns disease. provide a global stability analysis for model. determine value basic reproduction number R0 prove that disease-free equilibrium globally asymptotically stable if R0<1. If R0>1, disease free unstable unique endemi...

In this article, we introduce an infinite-dimensional deterministic metapopulation SIS model which takes into account the heterogeneity of infections and social network among a large population. We study long-time behavior dynamic. identify basic reproduction number R0 determines whether there exists stable endemic steady state (super-critical case: R0>1) or if only equilibrium is disease-free ...

In this paper we consider epidemic models of directly transmissible SIR (susceptible → infective → recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproducti...

OBJECTIVE To estimate the basic reproduction number (R0) of dengue fever including both imported and autochthonous cases. METHODS The study was conducted based on epidemiological data of the 2003 dengue epidemic in Brasília, Brazil. The basic reproduction number is estimated from the epidemic curve, fitting linearly the increase of initial cases. Aiming at simulating an epidemic with both aut...