In this paper, a periodic epidemic model is proposed in order to simulate the dynamics of pertussis transmission. We consider the waning of vaccine-induced immunity in the population. The basic reproduction number R0 is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if R0 < 1, and there exists at least one positive ...

We consider the problem of estimating the basic reproduction number R0 from data on prevalence dynamics at the beginning of a disease outbreak. We derive discrete and continuous time models, some coefficients of which are to be fitted from data. We show that prevalence of the disease is sufficient to determine R0. We apply this method to chronic wasting disease spread in Alberta determining a r...

We extend the Gröbner basis theory developed in [10, 11] to certain non-homogeneous, locally filtered finitely generated ideals in R0 , and to certain admissible orders. The main tool used is the study of two homogeneous ideals that may be associated to an ideal I R0 , namely the ideal grT (I) generated by all homogenous components of maximal degree of elements in I , and the “homogenized” idea...

One-flavour QCD – a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation – is studied by Monte Carlo simulations. The mass spectrum of hadronic bound states is investigated in a volume with extensions of L ≃ 4.4 r0 (≃ 2.2 fm) at two different lattice spacings: a ≃ 0.37 r0 (≃ 0.19 fm) and a ≃ 0.27 r0 (≃ 0.13 fm). The lattice action is Symanzik tree-level-imp...

We incorporate the immigration of susceptible individuals into an SEIR epidemic model, assuming that the immigration rate decreases as the spread of infection increases. For this model, the basic reproduction number, R0, is found, which determines that the disease is either extinct or persistent ultimately. The obtained results show that the disease becomes extinct as R0 < 1 and persists in the...

The global dynamics of a periodic SIS epidemic model with maturation delay is investigated. We first obtain sufficient conditions for the single population growth equation to admit a globally attractive positive periodic solution. Then we introduce the basic reproduction ratio R0 for the epidemic model, and show that the disease dies out when R0 < 1, and the disease remains endemic when R0 > 1....

In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibriu...

The basic reproduction number of an infection in a given population, R0, is inflated by individual heterogeneity in contact rates. Recently, new methods for estimating R0 using social contact data have been proposed. These methods, like most of their predecessors, ignore individual heterogeneity, and are sensitive to mis-specification of the contact function. Using a frailty framework, we deriv...

Let R = ⊕n≥0Rn be a homogeneous noetherian ring and let M be a finitely generated graded R-module. Let H R+(M) denote the i-th local cohomology module of M with respect to the irrelevant ideal R+ := ⊕n>0Rn of R. We show that if R0 is a domain, there is some s ∈ R0\{0} such that the (R0)s-modules H R+(M)s are torsion-free (or vanishing) for all i. On use of this, we can deduce the following resu...