A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

Abstract

The term public budget defects became nowadays a chronic, economical phenomenon, almost all the countries weather advanced or development country suffered from it, despite the different visions to economic schools of a thought to accept or reject the deficit in public budget but the prevailed opinion that is needed to rule the role of the state by reducing the public spending which led to continuous deficits in public budget and the consequent upon increase in government borrowing, increase taxes on income and wealth, thus weakening the in contrive for private investment which contributed to the increase of in flationary stagnation, it became a duty to state covered by the lack of financial sources

Encouraging micro-enterprises for comprehensive economic development are crucial to achieve the ambitious vision 2030 of the Kingdom of Saudi Arabia.

 Small and Medium enterprises are inputting around 15.5 per cent to GDP while 33 per cent contribution as a private sector to Saudi Arabia's gross domestic product (GDP). This study aims to identify the most important factors that affect the efficiency of small enterprises in Saudi Arabia. To accomplish this objective, the study was conducted for small projects via the comprehensive inventory method under the supervision of the Institute of Entrepreneurship. A total of 282 questionnaires were collected from entrepreneurs and the differentiation analysis

The research problem is dedicated to investigate reservoirs irrational economic behavior adopted by the ruling elites in developing countries about the investment methodology of human capital and operating policies is based on the terms of reference of economic theory and standards governing the market, which led to a chronic structural imbalance in the workforce structure and lack of consistency with different production structure, in turn, which had a reported effects in the emergence of the phenomenon of unemployment and that they involved a certain privacy, as has become the issues of unemployment and employment in the various countries of the world are issues more important due to the presence of large numbers of the workforce in th

The specialist researcher  fined the relations between economic ideas with economic facts in his theory which called humanity building it is appeared clearly ( in Ibn Khalduons’ Muqaddimah) in a clothe of economic  social  phenomenon's as a systematical analysis in all fifty chapters of al Muqaddimah ,therefore this paper deal with  Ibn Khalduon economic thoughts as important says which describe the society building in its economic subjective  and  examine the relationship between The dissert and the city within economic says which are cover  the social analysis ,and determinate   the analysis objects  which clearly in this dualism  model ,between the state and economic bas

Care and attention to the structure in the sixties of the last century replaced the mark, and if the structure of Ms. pampered in research and studies, it has become the mark is also a spoiled lady .. But the relationship between the structure and the mark was not a break and break, but the relationship of integration, His themes are structural analysis, and these are intellectual themes that can not be surpassed in contemporary research, especially since semiotics have emerged from the linguistic inflection.

We have tried to distinguish between text and speech, which is a daunting task, as it seems that whenever the difference between them is clear and clear, we come back to wonder whether the text is the same discourse, and is

         The Na-alginate bead is commonly used in biotechnology fields such as adsorption due to ion exchange between Ca and Na with elements. Scanning electron microscopy (SEM-EDX) has proven to be a comparative method in the detections of these adsorbed elements, but the un-flat forming area of beads that can introduce impossible of the detection of element adsorbed. In contrast, X-ray fluorescence (XRF) documents analysis of elements, direct examination, which may analysis the adsorbents of elements. Here, this Study evaluated the possibility by using XRF for the direct analysis for examples of Cd and Ag in a bench stand. This Study compared this to commonly use

Background: Gallstone disease (GSD) is a significant global health burden with variable prevalence influenced by metabolic, genetic, and infectious factors. Increasing evidence suggests that Gram-positive bacteria, particularly Staphylococcus aureus and Enterococcus species, contribute to gallstone pathogenesis through enzymatic activity and biofilm formation. Objectives: To characterize Gram-positive bacteria within gallstones from Iraqi patients, evaluate their biofilm-forming capacity, and analyze the relationship between bacterial colonization, gallstone type, and cholesterol levels. Methods: A total of 100 gallstones were obtained from patients undergoing elective cholecystectomy between October 2024 and March 2025. Stones were

Although the number of implants has increased gradually and consistently over the years to around one million per year globally, there is still far more potential for advancement in the field of dental implantology which is typically growing quickly. This study investigates the effect of nanofiller reinforcement high-performance polymer matrix to enhance mechanical and physical characteristics. Calcium silicate (CS)/Polyetherketoneketone (PEKK) biomedical composite (G0 as a control group) is reinforced with different weight percentages (G1-G4) of tellurium dioxide nanoparticles (TeO₂NPs) ( n = 5). This research uses ethanol as a binder for mixing various weight percentages (wt%) of TeO₂NPs w