In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that suppo

APFS Mohammed, 2014

     IR spectra of entrance and exit channels of methane and radical oxygen reaction are predicted in the ground state energy. Ab initio calculations at perturbation theory (MP2) with Dunning correction- consistent basis set (aug-cc-pVDZ) have been used. The calculations predicted structures, vibrational frequencies and potential energy surface. Three van der Waals minima from three adiabatic potential energy surfaces have been predicted in entrance and exit channels. Vibration frequency of 3209 cm^-1 and 3212 cm^-1 of C-H stretching in entrance structures are predicted while O-H vibrational frequency is predicted to be at 3673 cm^-1 in the other channel. The lowest energy structure in entrance

During the Maastrichtian, the rudists and benthic foraminifera of Aqra Formation underwent two major radiations, the first beginning in early Early Maastrichtian and peaking in the late Early Maastrichtian, and sconed extending from the early Late Maastrichtian to a late Late Maastrichtian peak.The radiations were punctuated and separated by prominent extinction episodes, fit with global Maastrichtian mass extinction.The high level of rudist, endemism [90%] allows definition of true regional origination and extinction pattern; these may represent global pattern for rudists. Radiation and extinction patterns in the northern Iraq [Kurdistan Region] can be variously related to relative sea level fluctuation and the rate of food and clastic

        This study included a group of (15) chronic renal failure patients (CRF), an addition group of (15) healthy individual  was concluded in this study for control. Trace and essential elements ( Zn, Cu , Ca , K , Na) were measured by atomic absorption and flam analyzer in sera of CRF patients pre and post dialysis and control groups. The results showed a significant ( p < 0.05) increase in Zn and k+ concentration in sera of CRF patients pre and post dialysis compared to the control group. While there is a significant decrease for copper concentration in sera of CRF patients pre and post dialysis compared to the control group.       There was no significant alte