In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat

The interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values

Malaysia will be an ageing population by 2030 as the number of those aged 60 years and above has increased drastically from 6.2 percent in 2000 and is expected to reach 13.6 percent by 2030. There are many challenges that will be faced due to the ageing population, one of which is the increasing cost of pensions in the future. In view of that, it is necessary to investigate the effect of actuarial assumptions on pension liabilities under the perspective of ageing. To estimate the pension liabilities, the Projected Unit Credit method is used in the study and commutation functions are employed in the process. Demographic risk and salary risk have been identified as major risks in analyzing pension liabilities in this study. The sensitivity

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This research aims to design a multi-objective mathematical model to assess the project quality based on three criteria: time, cost and performance. This model has been applied in one of the major projects formations of the Saad Public Company which enables to completion the project on time at an additional cost that would be within the estimated budget with a satisfactory level of the performance which match with consumer requirements. The problem of research is to ensure that the project is completed with the required quality Is subject to constraints, such as time, cost and performance, so this requires prioritizing multiple goals. The project

Abstract

The aim of the current research is to identify the level of availability of written expression skills included in the Arabic language curriculum document among middle school students from the teachers' point of view. The researcher used the descriptive approach. To analyze the data and access the research results, he used the (SPSS) program. The research was conducted during the first semester of the academic year 1442/1443 AH on a random sample of Arabic language teachers in the Bisha Education Department. They reached about (213) male and female teachers. The results revealed a number of indicators: the level of availability of written expression skills among middle school students in Bisha governorate

Abstract [email protected] Background: Acute Traumatic Stress Disorder (ATSD) might be complicated by Post Traumatic Stress Disorder (PTSD). Psychological First Aid (PFA) said to be helpful to reduce the possibility of reduction of ASD and PTSD symptoms. PFA is simple procedure to deliver help & support to victims, may be by some one close to him, quietly and professionally. Iraq has and is still experiencing, continuous traumatic stresses. ATSD is especially seen in war such as during the Gulf War, Embargo and nowadays under the current American occupation. With the extreme shortage of recourses and the given late priority to psychological problems and intervention have disastrous consequences on the psycho-social wellbeing of peop

Characterization of the heterogonous reservoir is complex representation and evaluation of petrophysical properties and application of the relationships between porosity-permeability within the framework of hydraulic flow units is used to estimate permeability in un-cored wells. Techniques of flow unit or hydraulic flow unit (HFU) divided the reservoir into zones laterally and vertically which can be managed and control fluid flow within flow unit and considerably is entirely different with other flow units through reservoir. Each flow unit can be distinguished by applying the relationships of flow zone indicator (FZI) method. Supporting the relationship between porosity and permeability by using flow zone indictor is ca

English allows for consonant sequences at the beginning of words, which poses a challenge for speakers of other languages, especially those whose native languages do not contain such sequences, such as Arabic. Therefore, this study aims to investigate students’ recognition and production of initial consecutive consonants in relation to gender, and the significance of the statistical differences between students in recognition and pronunciation of consecutive consonants. Consequently, a cohort of fifty-two Iraqi college students (18 males and 34 females) were selected as a sample. A multiple-choice test of two phases was used as a research instrument. The results showed that females outperformed males in recognizing and producing c