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This article discusses a dynamical analysis of the fractional-order model of HIV/AIDS. Biologically, the rate of subpopulation growth also depends on all previous conditions/memory effects. The dependency of the growth of subpopulations on the past conditions is considered by applying fractional derivatives. The model is assumed to consist of susceptible, HIV infected, HIV infected with treatment, resistance, and AIDS. The fractional-order model of HIV/AIDS with Caputo fractional-order derivative operators is constructed and then, the dynamical analysis is performed to determine the equilibrium points, local stability and global stability of the equilibrium points. The dynamical analysis results show that the model has two equilibrium points, namely the disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable when the basic reproduction number is less than one. The endemic equilibrium point exists if the basic reproduction number is more than one and is globally asymptotically stable unconditionally. To illustrate the dynamical analysis, we perform some numerical simulation using the Predictor-Corrector method. Numerical simulation results support the analytical results.

In this research, we discussed about optimal control of HIV/AIDS epidemic model with two latent stages, vertical transmission and treatment. In this model, the population is divided into five subpopulations, namely susceptible subpopulation, slow latent subpopulation, fast latent subpopulation, symptomatic subpopulation and AIDS subpopulation. The latent stage is divided into slow latent and fast latent stage depend on the condition of immune system which is different for each individual. Treatment (ART/antiretroviral) is given to infected individu in symptomatic stage. The rate of treatment from symptomatic stage to slow latent stage and to fast latent stage are set as u 1(t) and u 2(t) control variable, respectively. Here, the objective of optimal control is to minimize the number of infected as well as the cost of controls. The optimal control is obtained by applying Pontryagin’s Principle. In the end, we show some numerical simulations by using Forward-Backward Sweep Method. Numerical simulation result show that the combination of u 1 and u 2 control is the most effective control to reduce the number of infected/symptomatic subpopulation with minimum cost of controls.

Microbiology has an important role in solving human problems that are complex in many fields, such as environment, medical, and biotechnology. One of the important researches in microbiology fields is the counting of the number of bacterial colonies. This research is very important to estimate the number of bacterial cells in each millilitre or gram sample. However, the manual counting of bacterial colonies is a time-consuming task and is also very tedious. To help microbiologists, an automatic counting method of bacterial colonies based on bacterial colonies images is needed to be developed. However, the bacterial colonies images taking by the phones camera has low-quality. They are noise presence and lack of contrast, so the pre-processing method is necessary to be developed. This paper proposes the pre-processing method by using modified Perona-Malik Diffusion (PMD) and Contrast Limited Adaptive Histogram Equalization (CLAHE). The modified PMD filter is used to reduce noise, while the CLAHE method is used to enhance the contrast. Moreover, the morphology operators are used for the petri dish extraction and bacterial colonies counting process. The experimental results show that the proposed method has better performance than the original PMD based on the average values of precision, recall, and F-measure.

In this research, we develop a method to simulate nonsymmetric triple junction motion given by the gradient flow of surface energy with arbitrary surface tensions of the participating interfaces. The foundation of the method is the diffusion-based BMO algorithm in vector-valued formulation. We realize the nonsymmetric motion by generalizing the original BMO method and adding a corrective projection step. In the end, we show the numerical example for the simulation of the bubble motion using two different contact angles to simulate the contact angle dynamics., International Conference and Workshop on Mathematical Analysis and its Applications (ICWOMAA 2017)

博士論文要旨Abstract 以下に掲載予定：IAENG International Journal of Applied Mathematics. International Association of Engineers. 共著者：Nur Shofianah, Rhudaina Z. Mohammad, Karel Svadlenka