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As long as the field of Engineering, Science and Technology exists, the place of Mathematical modelling that involves stiff systems cannot be overemphasized. Models involving stiff system may result in ordinary differential equations (ODEs) or sometimes as system of ordinary differential equations which must be solved by experts working in that field.However, solving these models using analytical approach may sometimes be challenging or even near impossible. Therefore, it puts a great measure of importance on research into numerical algorithmsfor solution of this class of ordinary differential equations.Premised on the above mentioned, we have formulated, in this paper, a class of backward differentiation formula (BDF) which is a three-step numerical approximant for stiff systems of ODEs. The method was obtained through continuous collocation approach with Legendre polynomial as basis function. We incorporated three off-grid points at interpolation in order that we may retain theBDF’s single function evaluation characteristic. Analyzing basic properties of numerical methods led us to see that the method was consistent, having a uniform order six, zero-stable and in turn, convergent. The method's region of absolute stability was determined using the general linear method, which was plotted and shown to be stable over a vast area. The approach enumerates the solution of stiff of systems ODEs block by block using some discrete schemes that are secured from the corresponding continuous scheme. The method was tested using numerical experiments, and the results, when compared to exact or analytical answers as well as some methods published in the literature, proved that the method is efficient and accurate.

Background: Self-medication is widely practiced worldwide. Literatures abound on its use for medical ailments but there is paucity of information for dental complaints especially in Northeastern Nigeria. Hence, this study was designed to determine the prevalence of self-medication for dental problems before dental consultation and its associated factors among patients attending Federal Teaching Hospital (FTH), Dental and Maxillofacial Outpatient Clinic, Gombe, Gombe State, Nigeria. Materials and Methods: A descriptive cross-sectional study based on a structured pretested close-ended interviewer-administered questionnaire was distributed among adults visiting FTH outpatient dental clinic, Gombe, Nigeria for a period of 8 months. The questionnaire was composed of two main sections: demographic characteristics and questions assessing the behaviour of self-medication. The non-probability convenient sampling technique was used and data was stored and analysed using IBM-Statistical Package for Social Sciences (SPSS) version 23.0. Results: The results showed that the prevalence of self-medication was found to be 41.5% (194/468), with a higher prevalence among females (55.1% or 107/194) than males (44.9% or 87/194). The majority (52% or101/194) of the patients were in the 2-4th decades of life. Educational status was significantly associated with self-medication. Analgesics accounted for the greatest percentage (98/164 or 59.8%) of orthodox drugs used followed by antibiotics (62/164 or 37.8%). However, with respect to individual medication consumed, paracetamol accounted for the majority (28.7%). A greater number (55/194 or 28.4%) could not remember the name of the orthodox drugs they took before consultations. Street hawkers were the main source of these medicaments (36.6 or 71/194%). Fear of dental treatment (20.1% 39/194), ailment is simple and the need not to see a dentist (20.1% 39/194) were claimed to be the main reason for practicing self-medication with periodontitis (53.1% or 103/194), pulpitis (13.9% or 27/194) and pericoronitis (10.8% or 21/194) the main predictors. Conclusion: The prevalence of self-medications to dental problems in this study was discovered to be high with the use of both orthodox and unidentified traditional drugs. National Health Insurance Scheme should be made to cover all social group of Nigerians in order to encourage easy accessibilities of all people to wide range of medical and dental consultations, thereby discouraging the practice of self-medication.

Background: Recommendations by the Lancet Commission on Global Surgery regarding surgical care in low- and middle-income countries (LMICs) require development to address the needs of children. The Global Initiative for Children’s Surgery (GICS) was founded in 2016 to identify solutions to problems in children’s surgery by utilizing the expertise of practitioners from around the world. This report details this unique process and underlying principles. Methods: Three global meetings convened providers of surgical services for children. Through working group meetings, participants reviewed the status of global children’s surgery to develop priorities and identify necessary resources for implementation. Working groups were formed under LMIC leadership to address specific priorities. By creating networking opportunities, GICS has promoted the development of LMIC-LMIC and HIC-LMIC partnerships. Results: GICS members identified priorities for children’s surgical care within four pillars: infrastructure, service delivery, training and research. Guidelines for provision of care at every healthcare level based on these pillars were created. Seventeen subspecialty, LMIC chaired working groups developed the Optimal Resources for Children’s Surgery (OReCS) document. The guidelines are stratified by subspecialty and level of health care: primary health center, first-, second- and third-level hospitals, and the national children’s hospital. The OReCS document delineates the personnel, equipment, facilities, procedures, training, research and quality improvement components at all levels of care. Conclusion: Worldwide collaboration with leadership by providers from LMICs holds the promise of improving children’s surgical care. GICS will continue to evolve in order to achieve the vision of safe, affordable, timely surgical care for all children.

Background: Clefts of the orofacial complex are the second most prevalent birth defects anomalies. Management of children born with clefts is multidisciplinary with oral surgeons and orthodontists playing major roles. Objective: The aim of this study was to ascertain the occlusal anomalies in patients who had undergone cleft lip and palate repair. Methods: Data was collected from participants using a pretested anonymous structured questionnaire. An examination of their occlusions was carried out on the same day. All findings were recorded on a data sheet. Data were analyzed using the Statistical Package for the Social Sciences 20.0, and frequency tables of variables were generated. Significance was determined at a 95% confidence interval, and statistical significance was set at P

Orofacial clefts are the most common malformations of the head and neck. In Africa, orofacial clefts are underascertained, with little or no surveillance system in most parts for clefts and other birth defects. A Nigerian craniofacial anomalies study, NigeriaCRAN, was established in 2006 to support cleft research specifically for epidemiological studies, treatment outcomes, and studies into etiology and prevention. We pooled data from seven of the largest Smile Train treatment centers in the six geopolitical zones in Nigeria. Data from September 2006 to June 2011 were analyzed and clefts compared between sides and genders using the Fisher exact test. A total of 2197 cases were identified during the study period, with an estimated prevalence rate of 0.5 per 1000. Of the total number of orofacial clefts, 54.4% occur in males and 45.6% in females. There was a significant difference ( P=.0001) between unilateral left clefts and unilateral right clefts, and there was a significant difference ( P=.0001) between bilateral clefts and clefts on either the left or right side. A significant gender difference ( P=.03) was also observed for cleft palate, with more females than males. A total of 103 (4.7%) associated anomalies were identified. There were nine syndromic cleft cases, and 10.4% of the total number of individuals with clefts have an affected relative. The significant difference between unilateral clefts and the gender differences in the proportion of cleft palate only are consistent with the literature. The present study emphasizes the need for birth defects registries in developing countries in order to estimate the exact prevalence of birth defects including orofacial clefts.

Pleomorphic adenoma (PA) is the most common benign salivary gland tumor, accounting for up to 60% of all tumors of the salivary gland and 75–80% of all parotid tumors. It has a slow but progressive growth pattern and if untreated can become greatly enlarged in size. However, giant PA is uncommon. We report a case of giant parotid PA of more than 10 years duration in a 60‑year‑old male Nigerian. A 60‑year‑old male patient with 10‑year history of painless, massive, and pedunculated swelling in the left side of lower face measuring 25 cm × 23 cm × 17 cm in dimension. Computerized tomographic scan and percutaneous fine needle aspiration cytology returned a preliminary diagnosis of PA. Superficial parotidectomy with facial nerve preservation via the transcervical approach was performed. The excised mass weighed 5.5 kg while the postoperative healing was satisfactory. Benign PAs may attain a giant size if left untreated. Socioeconomic problems are some of the reasons for late presentation. Adequate excision of the tumor sparing the facial nerve is possible but intraoperative and reactionary hemorrhage are likely complications.Keywords: Challenges, developing country, giant, parotid, pleomorphic adenoma, salivary

Development of craniofacial structures is a complex process and disruption of any of the numerous steps can lead to development of oro-facial clefts. This is a surgically amenable anomaly as from early life that has had conflicting pattern of demographics reported by various researchers globally. There are several factors that are critical to the surgical outcome.Study the demographics and the management outcome of cleft lip, alveolus and palate and highlight factors responsible for improved care in recent time.Descriptive cohort study.Tertiary health institution.All consecutive patients managed for cleft lip, alveolus and palate (CLAP) over 7years and 10months were studied.Cleft lip, alveolus and palate repair was performed on 149 patients, January 1, 2001- December 31, 2008 with an incidence of 2.1/1000 live births. From this, 27 patients, averaging 4.5 patients per year were operated for the first 6 1/3 years while the remaining 122(81.9%) the next 1 1/2 years, averaging 81.6 patients yearly. Their ages ranged from 3 months - 60 years with 77 (51.7%) males and 72 (48.3.0%) females. Cleft lip was the main presentation in 108(72.5%) of which 72(66.7%) were left sided. Bilateral cleft lip were14 (9.4%). Five (3.4%) patients had associated anomalies out of which 3(60.0%) had CLAP while 2(40.0%) isolated cleft lip or palate. The technique for cleft lip repair was Millard's and Noordhoof's while palatal cleft was the two-flap palatoplasty with intravelar veloplasty. Success was recorded in 142(95.3%) with complication observed in 7(4.7%) patients.The rarity of cleft lip, alveolus and/or palate in the African native documented previously may no longer be tenable as observe in this study. Management outcome has improved owing to the collaboration with SmileTrain, USA, along with multidisciplinary approach.

Head and neck cancer is the 10(th) most common cancer in the world constituting 5-8% of total cancer burden in Europe and America. However, it is difficult to appreciate the burden in Nigeria because of inadequate data. This retrospective study analysed the clinicopathological variables of head and neck malignancies seen over a 10-year period at a northeastern Nigerian referral centre.The demographics and clinical findings of the patients were obtained from the case files while histology reports were retrieved from the histopathology department of the hospital. Malignancies involving the eye, brain and thyroid were excluded.One hundred and ninety five cases of head and neck malignancies were recorded over the ten year study period. The mean age of the patients was 38.3years (+20 SD) while a male: female ratio of 1.3:1 was recorded for all cases. The neck was the most frequent site of tumours, accounting for 57(29%) cases. While epithelial malignancies were 56.9% of all cases, lymphomas constituted 21.5%, sarcomas constituted 10.3% and others malignancies accounted for 11.3%. There was no sex predilection for carcinomas (1:1), but there were slightly more lymphomas 26(23%) in males than 16(19%) in females. Carcinomas were more prevalent in those above 51years of age; sarcomas were most common within the 21-30year age group while 42.8% of cases of lymphoma were in the 2(nd) and 3(rd) decades of life.While malignant head and neck tumours showed no sex predilection, carcinomas remained the most frequent head and neck malignancies in this study.

Objective: The aim of this study was to evaluate the relative frequencies, types and site distribution of oro-facial lesions in a North-Eastern Nigerian tertiary centre. Materials and Methods: The records of the Departments of Oral-Dental Surgery and Pathology of a tertiary hospital in Nigeria were reviewed and analyzed for patients with oro-facial lesions during a seven year period (January, 2001 - December, 2007). The main outcome measures were patients' age and sex, histology assessment, tissue type and location. Results: A total of 102 (51.3%) benign lesions, 59 (29.6%) malignant lesions and 38 (19.1%) inflammatory/reactive lesions were seen. The common benign neoplasms were ameloblastoma (23.5%), fibrous dysplasia (15.7%) and pleomorphic adenoma (13.7%). The malignant lesions were mainly well differentiated squamous cell carcinomas (28.8%) and terminal duct carcinoma (11.9%). Inflammatory lesions comprised mainly of chronic osteomyelitis (15.8%) and non-specific chronic inflammatory lesions; giant cell granulomas, granulation tissues which constituted 10.5% each. There were 104 (52.3%) males and 95 (47.7%) females giving a male: female ratio of 1.1:1. The mean age of the patients was 36.1(SD΁18.9) years with a range of 1 to 85 years. Most tissue specimens were soft tissues (61.3%), while bone specimen accounted for 15.6% of all specimens analysed. There were 62 (31.2%) mandibular lesions, 24 (12.1%) palatal lesions and 15 (7.5%) parotid lesions, while maxillary antral lesions were the least, constituting only 0.5% of all lesions studied. Conclusion: The range of diagnosed lesions from our study was diverse, though our results do not represent the actual prevalence of orofacial lesions within the general population, but simply reflect the frequency of histologically diagnosed lesions at a health center in North-East Nigeria. This survey has shown that most oro-facial lesions studied were benign neoplasms and that most of these neoplasms were from the mandible.