A SIMPLE LINEARIZATION PROCEDURE FOR OBTAINING R0 FROM INVASIVE EPIDEMIC MODELS

Plant diseases often cause yield losses in agriculture worldwide. In mathematical ecology, the concept of the basic (or basal) reproduction number, R₀, has received little attention in the scientific literature related to phytopathogen transmission in plants. The spread and magnitude of outbreaks, the rate of invasion and infectivity of the etiologic agent, the contact complexities occurring among parasite and host, and its susceptibility and period of infectiousness are very important factors for epidemiological models. These mathematical models, when applied in ecology, can help to understand the spread of infections from phytopathogens (or pests) to plant hosts as well as detect potential risks of contamination or outbreaks by using the basic reproduction number in effective control strategies. In this study, the Maclaurin series concepts on the Force of Infection were applied to derive R₀ expressions from generic epidemiological SIR (Susceptible‐Infected‐Removed) models. Consequently, we were able to obtain these relations from three transmission‐infection model examples. Then, once the expression of Force of Infection is known from the “infectious” problem studied, it is possible to apply this technique to formulate the R₀ relation and guide practicable strategies for dispersing invasive phytopathogen controls.     

Density dependence of the electric-field-gradient induced birefringence of the helium,neon and argon gases

An ab initio investigation of the density dependence of the electric-field-gradient induced birefringence (EFGB) for the noble gases helium, neon and argon is presented. To determine the second coefficient in the virial expansion of the molecular EFGB constant _mQ, the effect of two-body interactions has been studied by computing the internuclear dependence of the molecular quadrupole moment and of the dipole-dipole-quadrupole and dipole-magnetic dipole-dipole hyperpolarizabilities of the van der Waals dimers. A full-configuration-interaction approach as well as the coupled cluster singles and doubles and the coupled cluster singles and doubles plus perturbative triples approximations have been adopted, and extended basis sets including midbond functions have been employed. A semi-classical integration yields the virial coefficients. The effect of density for standard experimental conditions is found to be of the order of a few tens of parts per million for helium and neon, and of the order of a few parts per thousands for argon at low temperatures, and thus not detectable with present apparatus.     

Rotational spectrum of propylene oxide-neon

The free jet millimetre-wave absorption spectrum of the propylene oxide-Ne complex is reported for both the ²⁰Ne and ²²Ne isotopomers. The Ne atom lies on the same side as the methyl group (syn conformer) with respect to the plane of the COC ring. From the D_J centrifugal distortion constant the dissociation energy has been estimated to be about 1.1 kJ mol^?1.     

Rotational spectrum,dynamics and bond energy of 2,5-dihydrofuran—krypton van der Waals complex

The equilibrium conformation, dynamics and dissociation energy of the weakly bonded 2,5-dihydrofuran-Kr complex have been deduced from its free jet millimetre-wave spectrum. The equilibrium distance of Kr with respect to the centre of mass of the molecule is 3.61 Å, with Kr tilted 12.8° from the perpendicular to the centre of mass of the ring towards the oxygen atom. The dissociation energy is estimated from the centrifugal distortion constant D_J to be about 3.5kJ mol^?1.