This study presents a mathematical model describing the interaction of gut bacteria in the participation of probiotics and antibiotics, assuming that some good bacteria become harmful through mutations due to antibiotic exposure. The qualitative analysis exposes twelve equilibrium points, such as a good-bacteria equilibrium, a bad-bacteria equilibrium, and a coexisting endemic equilibrium in which both bacteria exist while being exposed to antibiotics. The theory of the Sotomayor theorem is applied to study the local bifurcation around all possible equilibrium points. It’s noticed that the transcritical and saddle-node bifurcation could occur near some of the system’s equilibrium points, while pitchfork bifurcation cannot be accrued at

The aim of the current research is to know the degree to which middle school teachers and female teachers in the southern border schools use electronic educational alternatives in the field of education from their point of view and its relationship to some variables, and to achieve this goal, a random sample of (200) teachers was selected in southern border schools, and a questionnaire was prepared to collect The data, as well as the descriptive approach was used to achieve this goal. T-test and analysis of variance were used for the statistical treatment. The results concluded that the educational courses provided to male and female teachers are not sufficient. It has also been concluded that the use of electronic educational alternativ

The implementation of the concept of project scheduling in the organizations generally requires a set of procedures and requirements, So, most important of all is the understanding and knowledge of the tools and techniques which are called the methods of scheduling projects. Consequently, the projects of the municipality administration in the holy governorate of Karbala suffer from the problem of delaying their projects and chaos in the ways of implementation. To provide assistance to this directorate and to demonstrate how to schedule projects using one of the advanced scientific methods that proved their ability to schedule any project and its potential to accelerate the time of completion, as well as ease of use and effectiven

The study of sex Structure and age characteristics of an important element of the
follow-up changes between different population groups, which are connected to a large degree
the demographic, social and economic characteristics, particularly since each population
group varying characteristics in terms of age, sex entail social, demographic, cultural and
economic implications, and from that the researcher has taken from Structure of sex and age
for population in the district of Tuz Khurmatu for (1997-2012 ) the subject of consideration
and maintain compared to see the contrast between them. Qualitative Research for installation
and the age of the urban and rural areas has touched the judiciary, as well as its respects

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient