Based on a simple model due to Dietz, it is shown that the size of a major epidemic of a vector-borne disease with basic reproduction ratio R0 > 1 is dominated by the size of a standard SIR (susceptible–infected–removed) epidemic with direct host-to-host transmission of disease and the same R0. Further bounds and numerical illustrations are provided, broadly spanning situations where the size o...

für die resultierende mittlere Geschwindigkeit eines Teilchens nach einem Stoß: t>red = v c p . Aus den Gesetzen des elastischen Stoßes für Kugeln der Massen m0, mx ergibt sich für die Geschwindigkeit von 77i0 nach dem Stoß mit ß = ( (m x m0 ) / (m, + m 0 ) ) 2, e=(l/ß-l) (d/R0)2 : v=v0(ßey*(( 1 + 1/fi) — cos2 ft)1'*; (A.6) cos #m i n = (1 (R0/d)2 (ß (vmJv 0)2)/ (ß-1) cos # m a x = (1 (R0/d)2)1...

In this work we deal with a class of second-order elliptic problems of the form − u = λk(|x |) f (u) in Ω , with non-homogeneous boundary condition u = a on ∂Ω where Ω is the ball of radius R0 centered at origin, λ, a are positive parameters, f ∈ C([0,+∞), [0,+∞)) is an increasing function and k ∈ C([0, R0], [0,+∞)) is not identically zero on any subinterval of [0, R0]. We obtain via a fixed po...

A general stochastic model for susceptible → infective recovered (SIR) epidemics in non-homogeneous populations is considered. The heterogeneity a very important aspect here since it allows more realistic but also complex models. basic reproduction number R0, an indication of the probability outbreak homogeneous does not indicate models anymore, because changes with initially infected case. The...

We use the Updated Zwicky Catalog of galaxies (Falco et al. 1999) to generate a catalog of groups, by means of a friend-of-friend algorithm. The groups identified have 4 or more members and a surrounding density contrast, δρ/ρ = 80. They cover the region −4 < δ < 90, |b| > 20 spanning over the radial velocity range of 2000 km s < cz < 15000 km s. The total sample (hereafter GUZC) comprises 517 ...

In this paper, we studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, R0, is derived. If R0 6 1, the disease-free equilibrium is globally stable and the disease always dies out. If R0 > 1, there exists a unique endemic equilibrium which is locally stable. Furthermore, we proved the global stability of the unique ...

We call F : {0, 1}n×{0, 1}n → {0, 1} a symmetric XOR function if for a function S : {0, 1, ..., n} → {0, 1}, F (x, y) = S(|x⊕ y|), for any x, y ∈ {0, 1}n, where |x⊕ y| is the Hamming weight of the bit-wise XOR of x and y. We show that for any such function, (a) the deterministic communication complexity is always Θ(n) except for four simple functions that have a constant complexity, and (b) up ...

A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R0 is computed and shown ...

In this paper, a simple parasite-host model proposed by Ebert et al.(2000) is reconsidered. The basic epidemiological reproduction number of parasite infection (R0) and the basic demographic reproduction number of infected hosts (R1) are given. The global dynamics of the model is completely investigated, and the existence of heteroclinic and homoclinic orbits is theoretically proved, which impl...

The basic reproductive ratio, R0, is a central quantity in the investigation and management of infectious pathogens. The standard model for describing stochastic epidemics is the continuous time epidemic birth-and-death process. The incidence data used to fit this model tend to be collected in discrete units (days, weeks, etc.), which makes model fitting, and estimation of R0 difficult. Discret...