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.

OMS-Vol. 3 (2019), Issue 3, pp. 210 – 216 Open Access Full-Text PDF

Abstract: 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.

OMS-Vol. 3 (2019), Issue 1, pp. 198 – 209 Open Access Full-Text PDF

Abstract: 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.