An Sveir Model for Assessing Potential Impact of an Imperfect Anti-SARS Vaccine

The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv). If Rv ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv \u3e 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming R0 = 4). Numerical simulations are used to explore the severity of outbreaks when Rv \u3e 1

Numerical Analysis of Defects Caused by Thermolysis in an Infinite Cylindrical Ceramic Moulding

The second-order parabolic (diffusion) equation, which governs the concentration of monomer during pyrolysis of a cylindrical ceramic moulding containing a polymer which degrades to monomer only, is solved: an infinite cylinder is considered. The method of lines is used to transform the partial differential equation into a system of first-order linear ordinary differential equations, the solution of which is seen to satisfy a recurrence relation. The concentration profile at a given time is computed by replacing the matrix exponential terms in this recurrence relation by a high-order Pade approximate. A parallel algorithm using two processors is developed by taking the partial fraction decomposition of the Pade approximate and a (matrix) rational expression in the recurrence relation

Numerical Methods for a Non-linear System Arising in Chemical Kinetics

Two numerical methods are proposed for the solution of a system of two dimensional reaction-diffusion equations with cubic non-linearity, known as the "Brusselator" system. The first method is derived using finite difference techniques and the solution is obtained in paralled using two processors running concurrently. The second method is based on a predictor-eorrector technique. This system of equations has important applications in chemical kinetics

Enzymatic pretreatment of grey cotion fabric for improving dye uptake, lustur and hand feel using fungal cellulase

Cellulase enzyme was extracted from pineapple peel substrate using Aspergiluss niger.  Because enzymes are sustainable alternatives to harsh toxic chemicals used in the Textile Industries. Cotton fabrics were treated with cellulase at variable concentrations at a pH of 5.5 and 55°C. Changes in various properties of the treated fabrics like weight loss, lusture, soft touch and overall dyeing properties were investigated. The results obtained show that cellulase have successfully removed staple fibres from the fabrics and thus, yield a glabrous appearance and soft touch of the treated fabrics; furthermore, it was established that percentage dye uptake and fastness properties of the fabrics were greatly improved as confirmed by the FTIR spectral analysis and UV- visible spectrophotometric analysis of the absorbance maximum of the dye liquor before and after dying.Key Words: Cellulase, Aspergillus niger, pre- treatment, cotton fabric and dye uptake

Comparison of ascorbic acid content of some selected fresh and dried tropical vegetables

Ascorbic acid (Vitamin C) was determined in four different tropical vegetables (Cucumber, Cabbage, Spinach and Tomatoes) sourced from Yankaba market, Kano state. Colorimetric method was used for the  determination. The ascorbic acid content in the cucumber, cabbage, spinach and tomatoes ranged from 51.67mgL-1 to 395.45mgL-1. Tomatoes were found to have the highest concentrations (395.45mgL-1) while cucumber has the lowest (181.82mgL-1 for the fresh and 60.00mgL-1 and 51.67mgL-1 respectively) for the dried vegetables. The deficiency of ascorbic acid is believed to result in scurvy, a disease characterized by spongy and sore gum, loose teeth, anaemia, swollen joint, fragile blood vessels. Frequent intake, therefore of these vegetables rich in vitamin C (especially tomatoes) will help prevent these problems in human being. This indicated that although the vegetables are rich in ascorbic acid content, their dried forms have grossly inadequate amount to ensure the provision of required dietary intake (RDI) of vitamin C for humans.Keywords: Ascorbic acid, Comparison, Vegetables, Vitamin

Incremental role of male circumcision on a generalised HIV epidemic through its protective effect against other sexually transmitted infections: from efficacy to effectiveness to population-level impact.

The protection of MC against STI contributes little to the overall effect of MC on HIV. Additional work is needed to determine whether, and under what conditions, the protective effect of MC efficacy against STIs can have a significant incremental benefit on the HIV epidemic

Mathematical assessment of the roles of age heterogeneity and vaccination on the dynamics and control of SARS-CoV-2

The COVID-19 pandemic, caused by SARS-CoV-2, disproportionately affected certain segments of society, particularly the elderly population (which suffered the brunt of the burden of the pandemic in terms of severity of the disease, hospitalization, and death). This study presents a generalized multigroup model, with m heterogeneous sub-populations, to assess the population-level impact of age heterogeneity and vaccination on the transmission dynamics and control of the SARS-CoV-2 pandemic in the United States. Rigorous analysis of the model for the homogeneous case (i.e., the model with m = 1) reveal that its disease-free equilibrium is globally-asymptotically stable for two special cases (with perfect vaccine efficacy or negligible disease-induced mortality) whenever the associated reproduction number is less than one. The model has a unique and globally-asymptotically stable endemic equilibrium, for special a case, when the associated reproduction threshold exceeds one. The homogeneous model was fitted using the observed cumulative mortality data for the United States during three distinct waves (Waves A (October 17, 2020 to April 5, 2021), B (July 9, 2021 to November 7, 2021) and C (January 1, 2022 to May 7, 2022)) chosen to align with time periods when the Alpha, Delta and Omicron were, respectively, the predominant variants in the United States. The calibrated model was used to derive a theoretical expression for achieving vaccine-derived herd immunity (needed to eliminate the disease in the United States). It was shown that, using the one-group homogeneous model, vaccine-derived herd immunity is not attainable during Wave C of the pandemic in the United States, regardless of the coverage level of the fully-vaccinated individuals. Global sensitivity analysis was carried out to determine the parameters of the model that have the most influence on the disease dynamics and burden. These analyses reveal that control and mitigation strategies that may be very effective during one wave may not be so very effective during the other wave or waves. However, strategies that target asymptomatic and pre-symptomatic infectious individuals are shown to be consistently effective across all waves. To study the impact of the disproportionate effect of COVID-19 on the elderly population, we considered the heterogeneous model for the case where the total population is subdivided into the sub-populations of individuals under 65 years of age and those that are 65 and older. The resulting two-group heterogeneous model, which was also fitted using the cumulative mortality data for wave C, was also rigorously analysed. Unlike for the case of the one-group model, it was shown, for the two-group model, that vaccine-derived herd immunity can indeed be achieved during Wave C of the pandemic if at least 61% of the populace is fully vaccinated. Thus, this study shows that adding age heterogeneity into a SARS-CoV-2 vaccination model with homogeneous mixing significantly reduces the level of vaccination coverage needed to achieve vaccine-derived herd immunity (specifically, for the heterogeneous model, herd-immunity can be attained during Wave C if a moderate proportion of susceptible individuals are fully vaccinated). The consequence of this result is that vaccination models for SARS-CoV-2 that do not explicitly account for age heterogeneity may be overestimating the level of vaccine-derived herd immunity threshold needed to eliminate the SARS-CoV-2 pandemic.The National Science Foundation.http://www.keaipublishing.com/idmhj2024Mathematics and Applied MathematicsSDG-03:Good heatlh and well-bein

Modeling the impact of quarantine during an outbreak of Ebola virus disease

The quarantine of people suspected of being exposed to an infectious agent is one of the most basic public health measure that has historically been used to combat the spread of communicable diseases in human communities. This study presents a new deterministic model for assessing the population-level impact of the quarantine of individuals suspected of being exposed to disease on the spread of the 2014–2015 outbreaks of Ebola viral disease. It is assumed that quarantine is imperfect (i.e., individuals can acquire infection during quarantine). In the absence of quarantine, the model is shown to exhibit global dynamics with respect to the disease-free and its unique endemic equilibrium when a certain epidemiological threshold (denoted by $\mathcal{R}_0$) is either less than or greater than unity. Thus, unlike the full model with imperfect quarantine (which is known to exhibit the phenomenon of backward bifurcation), the version of the model with no quarantine does not undergo a backward bifurcation. Using data relevant to the 2014–2015 Ebola transmission dynamics in the three West African countries (Guinea, Liberia and Sierra Leone), uncertainty analysis of the model show that, although the current level and effectiveness of quarantine can lead to significant reduction in disease burden, they fail to bring the associated quarantine reproduction number ($\mathcal{R}_0^Q$) to a value less than unity (which is needed to make effective disease control or elimination feasible). This reduction of $\mathcal{R}_0^Q$ is, however, very possible with a modest increase in quarantine rate and effectiveness. It is further shown, via sensitivity analysis, that the parameters related to the effectiveness of quarantine (namely the parameter associated with the reduction in infectiousness of infected quarantined individuals and the contact rate during quarantine) are the main drivers of the disease transmission dynamics. Overall, this study shows that the singular implementation of a quarantine intervention strategy can lead to the effective control or elimination of Ebola viral disease in a community if its coverage and effectiveness levels are high enough