Cervical cancer is a global threat with over half a million cases worldwide and over 200000 deaths annually. Sexual minority women are at risk for infection with human papillomavirus (HPV); the virus which causes cervical cancer, yet little is known about the prevalence of HPV infection. In this paper, the dynamics of HPV infection in the presence of vaccination among women which progresses to cervical cancer is investigated. The disease-free equilibrium state of the model is determined. Using the next generation method, the cancer reproduction number, \(R_0\), is computed in terms of the model parameters and used as a threshold value. The reproduction number is examined analytically for its sensitivity to the vaccination parameter having shown that it is locally and globally asymptotically stable for \(R_0<1\) and unstable for \(R_0>1\) at the disease free state. The centre manifold theorem is used to determine the stability of the endemic equilibrium and shown to exhibit a backward bifurcation phenomenon implying that cervical cancer due to HPV infection may persist in the population even if \(R_0<1\). Finally, numerical simulations are carried out to obtain analytical results. As prevalence estimates vary between sexual orientation dimensions, these findings help inform targeted HPV and cervical cancer prevention efforts.

The study of integral operators has always been important in the subjects of mathematics, physics, and in diverse areas of applied sciences. It has been challenging to discover and formulate new types of integral operators. The aim of this paper is to study and formulate an integral operator of a general nature. Under some suitable conditions the existence of a new integral operator is established. The boundedness of left and right sided integral operators is obtained and further boundedness of their sum is given. The investigated integral operators derive several known integrals and have interesting consequences for fractional calculus integral operators and conformable integrals. The presented results provide the boundedness of various fractional and conformable integral operators simultaneously.

In this paper, we study the oscillatory theory for fractional differential equations (FDEs) via \(\psi\)-Hilfer fractional derivative. Sufficient conditions are established for the oscillation of solutions FDEs.

In this article, we study some properties of the solutions of the following difference equation: \(x_{n+1}=a x_{n}+\dfrac{b x_{n} x_{n-4}}{cx_{n-3}+dx_{n-4}},\quad n=0,1,…\) where the initial conditions \(x_{-4},x_{-3}, x_{-2}, x_{-1}, x_0\) are arbitrary positive real numbers and \(a, b, c, d\) are positive constants. Also, we give specific form of the solutions of four special cases of this equation.

A deterministic model for the transmission dynamics of two-strains Herpes Simplex Virus (HSV) is developed and analyzed. Following the qualitative analysis of the model, reveals a globally asymptotically stable disease free equilibrium whenever a certain epidemiological threshold known as the reproduction number (\(\mathcal{R}_0\)), is less than unity and the disease persist in the population whenever this threshold exceed unity. However, it was shown that the endemic equilibrium is globally asymptotically stable for a special case. Numerical simulation of the model reveals that whenever \(\mathcal{R}_1<1<\mathcal{R}_2\), strain 2 drives strain 1 to extinction (competitive exclusion) but when \(\mathcal{R}_2<1<\mathcal{R}_1\), strain 1 does not drive strain 2 to extinction. Finally, it was shown numerically that super-infection increases the spread of HSV-2 in the model.

This work is concerned with the oscillatory behavior of fourth-order delay differential equation with middle term. By using the generalized Riccati transformations and new comparison principles, we establish new oscillation results for this equation. An example illustrating the results is also given.

Let \(G=(V,E)\) be a finite simple graph with \(v =|V(G)|\) vertices and \(e=|E(G)|\) edges. Further suppose that \(\mathbb{H}:=\{H_1, H_2, \dots, H_t\}\) is a family of subgraphs of \(G\). In case, each edge of \(E(G)\) belongs to at least one of the subgraphs \(H_i\) from the family \(\mathbb{H}\), we say \(G\) admits an edge-covering. When every subgraph \(H_i\) in \(\mathbb{H}\) is isomorphic to a~given graph \(H\), then the graph \(G\) admits an \(H\)-covering. A graph \(G\) admitting \(H\) covering is called an \((a,d)-H\)-antimagic if there is a bijection \(\eta:V\cup E \to \{1,2,\dots, v+e \}\) such that for each subgraph \(H’\) of \(G\) isomorphic to \(H\), the sum of labels of all the edges and vertices belongs to \(H’\) constitutes an arithmetic progression with the initial term \(a\) and the common difference \(d\). For \(\eta(V)= \{ 1,2,3,\dots,v\}\), the graph \(G\) is said to be super \((a,d)-H\)-antimagic and for \(d=0\) it is called \(H\)-supermagic. When the given graph \(H\) is a cycle \(C_m\) then \(H\)-covering is called \(C_m\)-covering and super \((a,d)-H\)-antimagic labeling becomes super \((a,d)-C_m\)-antimagic labeling. In this paper, we investigate the existence of super \((a,d)-C_m\)-antimagic labeling of book graphs \(B_n\), for \(m=4,\ n\geq2\) and for differences \(d=1, 2, 3, \dots,13\).

Matrix metalloproteinases-2 and -9 (MMP-2/-9) are key tissue remodeling enzymes that have multiple overlapping activities critical for wound healing and tumor progression. In search of new anti-tumor agents, indole-oxadiazole containing butanamides (1-5) were evaluated with B16F10 mouse melanoma cells in this study. The results showed that compounds 1, 2 and 3 inhibited the cell proliferation in a considerable manner at concentrations ranging from 0-44M. The possible migration inhibitory effects of these melanoma cells were further evaluated through gelatinolytic activity of MMP-2 and MMP-9 secreted from B16F10 cells and it was inferred that compounds 1, 2 and 3 affected the expression and activity of these enzymes in a dose dependent manner while compound 1 can be regarded as promising anti-tumor agent.

The under consideration study focuses on synthesis and characterization of Nickel oxide (NiO) nanoparticles. Nanosized Nickel oxide powder was successfully synthesized using a simple and low cast sol-gel method. This method is environment friendly requiring no expensive chemicals and is time saving. The sol-gel method was accompanied by the formation of precipitates which were dried and calcined at 550\(^{o}\)C to get nickel oxide nanoparticles. The synthesized nanopowder was characterized by X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), and Energy Dispersive Spectroscopy (EDX).

The graphene and graphene oxide are latest and advanced materials with wide applications in environment, medical applications, industries, defense applications. We have synthesized graphene oxide from graphite flakes by modifying Hummer method in which we used NaNO\(_{2}\) instead of NaNO\(_{3}\). Then we characterized our samples with X-Ray Diffractometry (XRD), Scanning-Electron Microscopy (SEM) and Fourier-Transform Infrared-Spectroscopy (FT-IR). These results confirmed the formation of graphene oxide also through this process. This graphene oxide can further be used for future applications in wastewater treatment and biomedical applications.