Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years

Optimal Control in Coupled Within-host and Between-host Models

We formulate an immuno-epidemiological model of coupled “within-host” model of ODEs and “between-host” model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the “between-host” model is established, and an explicit expression for the basic reproduction number of the “between-host” model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained

Chemical and Orgarnoleptic Quality of Figs from Selected Sweet bananas (Musa Spp)

The chemical composition and organoleptic quality of four Cameroonian industrial banana varieties at two ripening stages and figs made from them, were evaluated. The results showed that sucrose content and Lovibond colour index increased significantly with ripening in both fresh fruits and figs and appeared to be the main factors that influenced the appreciation of the quality of the figs. Of the four varieties evaluated for appearance, bitterness, texture, odour and taste, figs from Gros Michel were the most appreciated with respect to all the parameters put together The Journal of Food Technology in Africa Volume 5 Number 2 (April - June 2000), pp. 70-7

Optimal control in coupled within-host and between-host models

We formulate an immuno-epidemiological model of coupled within-host model of ODEs and between-host model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the between-host model is established, and an explicit expression for the basic reproduction number of the between-host model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained. © EDP Sciences, 2014

The Effect of Bone Ash on the Physio-Chemical and Mechanical Properties of Clay Ceramic Bricks

Bone ash waste can be used to fabricate clay ceramic bricks, consequently managing their pollution of the environment. This is because bone ash (BA) and clay predominantly consist of calcium and alumina-silicate, respectively, which are components of clay ceramic brick (CCB) materials. This study aims to investigate the effect of bone ash and temperature on the physio-chemical and mechanical properties of CCB. Different percentages of bone ash (5%, 10%, 15%, and 20%) were added to clay and heat treated at temperatures of 100 °C, 300 °C, 600 °C, and 900 °C, and their compressive strengths were measured. Prior to the determination of their mechanical properties, the CCB chemical and phase compositions were characterized using FTIR spectroscopy and X-ray diffraction (XRD). The CCB microstructure was evaluated with scanning electron microscopy (SEM) and the compressive strength was tested. The results suggest that the addition of bone ash (10% and 15%) improves the compressive strength and water absorption properties after heat treatment of CCB at higher temperatures

Optimal Control in Coupled Within-host and Between-host Models

We formulate an immuno-epidemiological model of coupled “within-host” model of ODEs and “between-host” model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the “between-host” model is established, and an explicit expression for the basic reproduction number of the “between-host” model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained