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In the field of microbiology, the counting of bacterial colonies is fundamental and mandatory. This is done to estimate the number of bacterial cells in every 1 milliliter or gram of sample. The counting takes a long time and is tedious, so it requires an accurate and fast counting method. The image quality used is very low and contains noise. Therefore, a preprocessing method is needed to reduce the noise. The Perona-Malik filter method is known to be able to remove noise well. However, it is difficult to determine the appropriate gradient threshold parameter ( ) for each different image. To find the appropriate value of , the original Sobel Mask method and Sobel Mask Fractional-Order are used to estimate the value of . The experimental results show the results of noise reduction using PMD with a value of from the original Sobel Mask and Sobel Mask Fractional-Order. The results of the accuracy of determining the value of k with the Sobel Mask Fractional-Order (α=1.0) show higher results based on the F-Measure values for samples 1, 2, and 3 respectively 97%, 98%, and 90%.

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.