In this paper, we analyze a new continuous-time epidemic model including nonlinear delay differential equations by using parameters and functions selected from a class of intervals whose algebraic basis is based on quasilinear spaces. The main idea in the model’s generic structure is based on uncertainties in the values of parameters and functions forming the model. Therefore, using an interval coefficient approach rather than the exact value of parameters and functions that define transmissions between the compartments in the population dynamics will better represent the reality. Furthermore, preferring such an approach provides more realistic scenarios for temporal and stability dynamics of a population exposed to a disease. In this study, the quasilinear space is defined to explain the mathematical background of the interval approach in the fictional chain of the model. Next, descriptions belonging to the introduced model are included. After this compartmental system is presented as two systems formed by the lower and upper endpoints of the intervals determining parameters and functions, local and global dynamics related to stabilities of the models are analyzed separately for each. Then, using some interval analysis and functional analysis methods, these results are combined, and a conclusion about the stability of the proposed epidemic model has been reached. Alongside, the performance of the proposed approach is demonstrated by a visual simulation.

The inverse sum indeg index \(ISI(G)\) of a graph is equal to the sum over all edges \(uv\in E(G)\) of weights \(\frac{d_{u}d_{v}}{d_{u}+d_{v}}\). This paper presents the relation between the inverse sum indeg index and the chromatic number. The bounds for the spectral radius of the inverse sum indeg matrix and the inverse sum indeg energy are obtained. Additionally, the Nordhaus-Gaddum-type results for the inverse sum indeg index, the inverse sum indeg energy and the spectral radius of the inverse sum index matrix are given.

Analytical expressions for the steady-state solutions of modified Stokes’ second problem of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are determined when the gravity effects are considered. Fluid motion is generated by a flat plate that oscillates in its plane. We discuss similar solutions for the simple Couette flow of the same fluids. Obtained results can be used by the experimentalists who want to know the required time to reach the steady or permanent state. Furthermore, we discuss the accuracy of results by graphical comparisons between the solutions corresponding to the motion due to cosine oscillations of the plate and simple Couette flow. Similar solutions for incompressible Newtonian fluids with power-law dependence of viscosity on the pressure performing the same motions and some known solutions from the literature are obtained as limiting cases of the present results. The influence of pertinent parameters on fluid motion is graphically underlined and discussed.

In analogy with the classical theory of filters, for finitely complete or small categories, we provide the concepts of filter, \(\mathfrak{G}\)-neighborhood (short for “Grothendieck-neighborhood”) and cover-neighborhood of points of such categories, to study convergence, cluster point, closure of sieves and compactness on objects of that kind of categories. Finally, we study all these concepts in the category \(\mathbf{Loc}\) of locales.

Aim: To assess cases of dengue fever in Pediatric patients.
Methodology: Sixty-eight pediatric cases of dengue of both genders were included in the study. Clinical features and laboratory findings were recorded. Statistical analysis was performed using appropriate tests.
Results: Out of 68 patients, boys were 38, and girls were 30. Common symptoms were fever in 95%, vomiting in 68%, loose stools in 22%, periorbital puffiness in 10% and respiratory distress in 26, pain abdomen in 47% cases. The mean hemoglobin level at admission was 12.6 gm% and at discharge was 12.7gm%. The mean TLC was 56210 cumm of blood at admission, and at discharge was 122452 cumm of blood.
Conclusion: Common symptoms were fever, vomiting, respiratory distress and pain abdomen. Hence careful evaluation of dengue in children is required.

Aim: To assess relation between diabetes mellitus and thyroid dysfunction.
Methodology: 105 type II diabetes mellitus patients of both genders were included. Serum TSH (Thyroid Stimulating Hormone), free \(T_3\) (Triiodothyronine) and free \(T_4\)(Thyroxine) were determined in all enrolled patients.
Results: There were 50 males and 55 females in the present study. Age group 21-30 years had 15 patients, 31-40 years had 26, and 41-50 years had 64 patients. Duration of diabetes was 8.4 years, and the level of glycosylated hemoglobin (HbA1C) was 9.2 years. A significant difference was observed (P< 0.05). Serum T3 was increased by 15% and decreased by 4%. Free T3 was increased in 5% and decreased in 13%, and free T4 was increased in 7% and decreased in 5%. There were 20 hypothyroidism and 29 hyperthyroidism patients. Maximum hypothyroidism patients (12) and hyperthyroidism patients (14) were seen with >7 HbA1C levels.
Conclusion: Most of the type II DM patients had hypothyroidism than hyperthyroidism.

Aim: To assess cases of pregnancy induced hypertension.
Materials & Methods: Our study included 74 cases of pregnancy-induced hypertension. Parameters such as age, marital status, education, parity, etc., were recorded.
Results: Age group (years) <20 had 30%, 20-24 had 45%, 25-29 had 16%, 30-34 had 5% and >35 had 4% cases. Education level was illiterate in 40% and literate in 60%, and marital status was married in 58%, single in 26% and divorced in 16$, parity was 0 in 24%, 1-2 in 46% and >2 in 30%, gravida was primi in 40% and multi in 60%, previous PIH was seen in 24% patients. Family history of DM was observed in 25%, family history of PIH in 18%, family history of hypertension was seen in 10%, history of asthma was seen among in 8\% and history of kidney disease 30% patients. The difference was significant (P< 0.05).
Conclusion: Common risk factors of pregnancy induced hypertension was family history history of asthma, hypertension, family history of PIH, family history of DM, history of kidney disease.

In the presented work we applied three machine learning techniques to forecast and predict COVID-19 cases, deaths ad recoveries numbers in Algeria for the next six months using data from February 25th, 2020 to April 26th , 2021. These models are represented by the Gaussian process regression (GPR), the support vector machine (SVM) and the decision tree (DT). The plotting results and parameters evaluation pointed out that the Gaussian Process Regression (GPR) has the best performance. Prediction with this model showed that the number of cases, deaths and recoveries will increase in the next months Algeria recording a peak in the month of August and the curve will tend to decrease later.

This paper presents the spectral reflectance of thermally evaporated ZnS/Ag nanostructures. The coating of ZnS/Ag nanostructures was performed in two steps while varying the film thickness and deposition angle. Silver metal wire (99.99% purity) was heated under vacuum at a pressure of \(2.5 \times 10^{-5}\) mBars and deposited on glass slide substrates in the diffusion pump microprocessor vacuum coater (Edwards AUTO 306). Pieces of zinc sulphide (99.99% purity) were heated and deposited to the glass slides previously coated with silver to form the ZnS/Ag/glass composite. The optical reflectance of the samples was studied by the UV/Vis/NIR spectrometer (Perkin Elmer Lambda 19) with UV-WinLab software. The reflectance was measured at angles of incidence between \(15^o\) and \(75^o\). Spectrophotometric studies showed that reflectance decreased with decrease in film thickness and decreased with increase in deposition angle of silver nanoparticles. The reflectance of ZnS/Ag nanostructures decreased with increase in deposition angle of zinc sulphide.

This paper discusses a gallery of useful results in connection with integrating factors that are often left as problems for discovery learning and are generally not taught in typical Ordinary Differential Equations courses. Most often than not the approach earlier writers employ is to give a possible form for an integrating factor that may results in an integrating curve without practical prove as far as the subject matter is concerned. In this write-up, an attempt is made by solving the resulting partial differential equation emanating from an underlining general differential equation of a non-exact form, by the use of the ratio theorem to establish various intricate possibilities of integrating factors that are seldom and often relegated to the background, even though they may be equally be applied as a function of a unitary variable or a linear combination of both the dependent and independent variables under certain conditions. Granted an integrating factor is found and such a function applied, the benefit is enormous especially the non-exact differential equation reduces into a known type which may be identified as exact, homogeneous, and or separable that yields a solution.