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We present a new way of constructing a fractional-based convolution mask with an application to image edge analysis. The mask was constructed based on the Riemann-Liouville fractional derivative which is a special form of the Srivastava-Owa operator. This operator is generally known to be robust in solving a range of differential equations due to its inherent property of memory effect. However, its application in constructing a convolution mask can be devastating if not carefully constructed. In this paper, we show another effective way of constructing a fractional-based convolution mask that is able to find edges in detail quite significantly. The resulting mask can trap both local discontinuities in intensity and its derivatives as well as locating Dirac edges. The experiments conducted on the mask were done using some selected well known synthetic and Medical images with realistic geometry. Using visual perception and performing both mean square error and peak signal-to-noise ratios analysis, the method demonstrated significant advantages over other known methods.

In this paper, a Susceptible -Exposed -Infected -Recovered (SEIR) epidemiological model is formulated to determine the transmission of tuberculosis. The equilibrium points of the model are found and their stability is investigated. By analyzing the model, a threshold parameter R 0 was found which is the basic reproductive number. It is noted that when R 0 < 1 the disease will fail to spread and when R 0 > 1 the disease will persist in the population and become endemic. The model has two non-negative equilibria namely the disease -free equilibrium and the endemic equilibrium. The graphical solutions of the differential equations were developed using Matlab as well as the computer simulations.

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

A simplified mathematical model of immune responds to Hepatitis B Virus (HBV) infection is presented. This focuses on the control of the infection by the interferons, the innate and adaptive immunity. The model was compartmentalized as appropriate and the resulting model equations were solved numerically. A mathematical analysis of the model shows that both disease-free and endemic equilibrium point exist and we derive conditions for their stability. We perform sensitivity analysis on the model parameters, to account for the variability and speed of adaptation