Mathematical Model for Ebola Virus Infection in Human with Effectiveness of Drug Usage

In this paper, we formulated a mathematical model of the dynamics of Ebola virus infection incorporating effectiveness of drug usage. The infection free and infection persistence equilibrium points were obtained. The control reproduction number was obtained which was used to analyse the local and global stability of the infectionfree equilibrium. Using the method of linearization, the infection-free equilibrium (IFE) state was found to be locally asymptotically stable if Rc < 1 and unstable if Rc > 1. By constructing lyapunov function, the infection-free equilibrium was found to be globally asymptotically unstable if Rc > 1. Numerical simulation of the model was done. It is observed that, as percentage of effectiveness of drug administration increases, the control reproduction number decreases. This suggests that with the help of drugs usage, the immunes system have the ability to suppress the increase of infected cells, as well as virus load which shown that the virus does not maintain an infection in the system.Keywords: Drug Usage; Ebola virus; Global stability; Immune response; Mathematical mode

Local Stability Analysis of an Infection-Age Mathematical Model for Tuberculosis Disease Dynamics

An infection age structured mathematical model for tuberculosis disease dynamics is investigated in this paper. The infectious population is structured according to time and age of infection. An explicit formula for the basic reproductive number, R0 of the model is obtained. We showed that the disease-free equilibrium (DFE) state is locally asymptotically stable if R0 < 1 and unstable if otherwise. This simply means that tuberculosis could be controlled in a population when the basic reproduction number is less than unity.Keywords: Basic reproduction number; Infection-age; Local Stability; Tuberculosi

Mathematical Modeling of Effect of Pumping Rate on Contaminant Transport in Riverbank Filtration System

Riverbank filtration (RBF) is a natural technology that is used for river water treatment. This research seeks to investigate the effect of pumping rate on the transport of colloids in RBF. However, this work considered Dissolved Organic Matter (DOM) as a nutrient for bacteria. The mathematical model consists of groundwater flow equation and colloids concentration equations. The equations were solved analytically using parameter expanding method and Eigen function expansion techniques. The results obtained are presented graphically and discussed. It was observed that increase in pumping rate value enhance both the hydraulic head and concentration of colloids which slightly reduces the quality of pumped water from RBF

Co-infection Model Formulation to Evaluate the Transmission Dynamics of Malaria and Dengue Fever Virus

A mathematical model of the co-infection dynamics of malaria and dengue fever condition is formulated. In this work, the Basic reduction number is computed using the next generation method. The diseasefree equilibrium (DFE) point of the model is obtained. The local and global stability of the disease-free equilibrium point of the model is established. The result show that the DFE is locally asymptotically stable if the basic reproduction number is less than one but may not be globally asymptotically stable

A Mathematical Model and Simulation of Lime Shaft Kilns

In this paper a mathematical model to predict the heat transfer in a lime kiln is presented. We assume the reaction is not well-stirred. We examine the properties of solution under certain conditions. The governing equations are solved analytically using high activation energy asymptotics. Results are presented and potential implications are discussed.Keywords: lime shaft kiln, lime production, calcinations, simulation, shaft furnacesJournal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 91 – 9

Mathematical modelling of the calcination process

High quality lime is an essential raw material for Electric Arc Furnaces and Basic Oxygen Furnaces, steelmaking, alumina production etc. Decrease in fuel consumption in metallurgical furnaces is a tremendous opportunity for reduction of greenhouse gas emissions into the atmosphere. In this paper, a mathematical model of calcination process was studied. An analytical solution is obtained for the model. From the numerical simulation, it is observed that the gas temperature increases as the activation energy and Frank-Kamenetskii parameter increases. It is also observed that the material temperature decreases with increase in activation energy while it is increaseswith increase in Frank-Kamenetskii parameter

A mathematical model of combustion kinetics of municipal solid waste (MSW)

Municipal Solid Waste has become a serious environmental problem troubling many cities. In this paper, a mathematical model of combustion kinetics of municipal solid waste with focus on plastic waste was studied. An analytical solution is obtained for the model. From the numerical simulation, it is observed that the heating rate is proportional to the heating temperature and the conversion rate of the system. It is also observed that the conversion rate increases as the pre-exponential factor increases while it decreases as the activation energy and reaction order increases