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.

OMS-Vol. 3 (2019), Issue 1, pp. 191 – 197 Open Access Full-Text PDF

Abstract: 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.

OMS-Vol. 3 (2019), Issue 1, pp. 184 – 190 Open Access Full-Text PDF

Abstract: 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 \(d=1, 2, 3, \dots,13\).