OMS-Vol. 3 (2019), Issue 3, pp. 256 – 261 Open Access Full-Text PDF

Abstract: In ring \(\mathbb{R}=\mathbb{Z}_{2}+u\mathbb{Z}_{2}+u^2\mathbb{Z}_{2}\) where \(u^3=0,\) using Lee weight and generalized Lee weight, some lower bound and upper bound on the covering radius of codes is given and also to find the covering radius for various repetition codes with respect to same and different length in \(\mathbb{R}.\)

OMS-Vol. 3 (2019), Issue 3, pp. 245 – 255 Open Access Full-Text PDF

Abstract: There has been much debate about the role Vitamin C plays in the innate immune response, and if it has the potential to be used as a drug to combat conditions in which the immune system is compromised, from the common cold to cystic fibrosis. Here, the author creates a basic model of the innate response, capturing the dynamics among phagocytic cells, host cells, foreign virus/bacteria, and Vitamin C. Through mathematical simulations, the author concludes that Vitamin C can be used as a stand-alone drug to eradicate a viral/bacterial infection if given constant infusions. If this is not possible due to other side effects that may harm the patient, Vitamin C may be used in quick succession with another anti-bacterial/anti-viral medication to aid the patient. This, moreover, could help minimize the amount of side effects of the anti-bacterial/anti-viral drug and slow down bacterial evolution. Finally, the author modifies the system to simulate cases of renal failure, acute lung injury, liver damage, chronic granulomatous disease, and the Chédiak-Higashi syndrome, showing how Vitamin C can help individuals with these diseases.

OMS-Vol. 3 (2019), Issue 1, pp. 234 – 244 Open Access Full-Text PDF

Abstract: In the 3-dimensional Euclidean space \(\mathbb{E}^{3}\) and Lorentzian-Minkowski space \(\mathbb{E}_{1}^{3},\) a translation and homothetical TH-surface is parameterized \(z(u,v)=A(f(u)+g(v))+Bf(u)g(v),\) where \(f\) and \(g\) are smooth functions and \(A\), \(B\) are non-zero real numbers. In this paper, we define TH-surfaces in the 3-dimensional Euclidean space \(\mathbb{E}^{3}\) and Lorentzian-Minkowski space \(\mathbb{E}_{1}^{3}\) and completely classify minimal or flat TH-surfaces.

OMS-Vol. 3 (2019), Issue 3, pp. 217 – 233 Open Access Full-Text PDF

Abstract: 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.