Mathematics

In this paper we introduce the notion of Boolean like ring extension(for short, BLR extension) of a group and obtain various properties. We show that any BLR extension of a group is a group. Further, scalar multiplication on any BLR extension of a group is defined and studied certain properties.

In this paper, the spatiotemporal dynamics of a modified Leslie-Gower predator-prey system with Beddington -DeAngelis functional response incorporating constant proportion of prey refuge under homogeneous Neumann boundary condition is investigated. The local and global asymptotic stability of the unique positive homogeneous steady state in the absence of diffusion are discussed. Furthermore, we perform a series of numerical simulations and the results of the numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripe like or spotted or coexistence of both..

A three species food web comprising of two preys and one predator in an isolated homogeneous habitat is considered. The preys are assumed to grow logistically. The predator follows modified Leslie-Gower dynamics and feeds upon the prey species according to Holling Type II functional response.
The local stability of the constant positive steady state of the corresponding temporal system and the spatio-temporal system are discussed. The existence and non-existence of non- constant positive steady states are investigated.

The 2014/2015 Ebola epidemic in West Africa is the leading ever recorded, and identifying the integrated and applicable dynamics of public health intervention is a key concern, both for current and future epidemics. Moreover, as transmissibility and mortality are supposed to increase as symptoms progress, intervention approaches may depend on individual’s stage of infection. To inspect these issues, we develop SEIIsR mathematical model that study the control mechanism and spread of Ebola epidemic by reducing Is compartment. This work is intensively analysis the sensitive model parameters, disease free equilibrium point locally and globally asymptotically stability, existence of endemic equilibrium point, simulation study and data fitting. A variety of intervention measures exist to prevent and control epidemic diseases. In this study Isolation and contact tracing are proposed. Isolation is an important control strategy for containing Ebola epidemics. The analysis showed that if the most essential epidemiological parameter so called basic reproductive number R0 < 1 then disease free equilibrium point is stable whereas endemic equilibrium point is exist and stable if R0 > 1. The result indicated that early case detection followed by strict isolation could control Ebola outbreak. Tracing close contacts of cases and contacts of exposed health care workers additionally reduces the number of new infected cases. The study emphasizes the significance of early identification and isolation of Ebola cases to reduce the number of people getting infected. According to the numerical solution early identification or Isolated from Exposed is more significance than infected compartment. The best investigation of this study acknowledged that, it is possible to control the outbreak with short period of time by using effective contact tracing and isolation even if the value of R0 > 1. In SEIIsR model the best fit of cumulative infected case in West Africa is computed to follow simulated curve with R0 = 1.3. Further, the study supports the cumulative death cases due to Ebola epidemic is 63% of the infected individuals. Without intervention Ebola epidemic spread is going on where R0 > 1 whereas it is die out where R0 < 1. If we isolate more than 30% of exposed and infected individuals it is possible to reduce and vanish the epidemics spread.

BACKGROUND: Antenatal depression is one of the common problems during pregnancy with a magnitude of 20% to 30% globally. It can negatively endanger women's and off springs lives. As there are scarce reports on this area in Northern Ethiopia, it is important to carry out different studies that explore the magnitude of the problem and related factors in rural areas. The aim of this study is thus to assess the magnitude of antenatal depressive symptoms and associated factors among women at Maichew Town, North Ethiopia. METHODS: A facility based cross sectional study was conducted among 196 pregnant women from April to June 2015. Pregnant women who had antenatal care follow-ups at the public health facilities were included in the study. Through proportional allocation to each facility, systematic random sampling technique was used to select the study participants. We used the local language version of Beck Depression Inventory to assess depressive symptoms with a cutoff point of 14 or more. Data was collected by trained Psychiatric Nurses; data entry and analysis were processed by SPSS window 20. The level of significance was determined using odds ratio and 95% confidence interval. RESULT: About 16.3% of the participants had never given birth before, and 46.4% and 42.3% were in the third and second trimesters of pregnancy respectively. Unwanted pregnancy was reported by 25.5% of the participants. Among those with previous pregnancy, 7.1% had previous obstetric complication. The magnitude of depression was 31.1%. Pregnant women with low level of income (AOR=3.66 (95%CI; 1.12, 11.96)), unmarried (AOR=4.07 (95% CI; 1.18, 14.04)) and house wives (AOR= 4.24 (1.38, 13.03)) were risk groups for depression. CONCLUSION: Antenatal depression is a common problem; thus screening activities of depression in antenatal care services should be emphasized with more concern to unmarried women, those with low level of income and house wives.

Background: Substance abuse is a serious problem that interferes with an individual's physical and mental health, on the individual social situation and responsibilities. Of the young segment of the Ethiopian population, college and university students are the most at risk of using psychoactive substances. Its use among adolescents can be harmful, leading to decreased academic performance, increased risk of contracting HIV/AIDS including sexually transmitted diseases, and psychiatric disorders. Hence a need to conduct studies in this issue is fundamental and with the aim of determining the magnitude of psychoactive substance use among University students at Adigrat, this investigation was conducted. Methodology: An institution based cross sectional study design using quantitative method was employed on 161 students; and after stratifying for department and batch, systematic random sampling was used to select study subjects. The study period was from April 1 to June 20, 2014. Data was gathered by anonymous self-administer questionnaire using ASSIST and CAGE tools; also abuse was determined at a score of ≥ 2 on CAGE. Result: The magnitude of substance abuse was 16.7%. The commonly abused substances were alcohol (8.7%) followed by Khat (6.7%); and cigarettes were abused by 6% of the participants. Comparably 3.33% and 2% were cannabis and cocaine abusers respectively. Peer pressure 29 (34.52%), family pressure 25 (29.76%), availability of the substances 17 (20.24%), including religious purpose 3 (3.57%) were common reasons to initiate extracting substances. In addition nearly half of them started using substances at the primary school level. Recommendation: It is important to design suitable policies, culturally and psychologically appropriate intervention packages so as to tackle multiple effects of psychoactive substance abuse among University students.

This study reviews the impact of climate change and variability on crop production mainly on rain fed agriculture in Wolayta Zone. In all nine stations daily climate data were collected from NMSA and aggregated to monthly. The monthly rainfall was varied and distributed moderately on annual and seasonal basis in all stations. The occasion of onset dates are slightly increasing (delaying) for both stations toward the recent years. The end dates of the growing season were decreasing at Wolayta station and very slightly increasing at Bilate station. The interannual variability of length of growing season for both the stations was low. In both the stations, the dry spell length probability of longer than 5, 7 and 10 days were decreasing from the starting date of the growing season to the middle of Belg season and increasing towards the end of Belg Season. SDSM is applied in order to downscale the climate variables at the station level. Under A2 scenario, SDSM indicates an increase in th...