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.

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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.

This research focus on dynamical analysis of a SIQRVB (Susceptible-Infectious-Quarantined-Recovered-Vaccinated-Bacterial) model. It describe the spread of cholerae with quarantine, vaccination and two transmission paths. As is well-known, there mainly exist two transmission paths for cholerae: environment-to-human transmission and human-to-human transmission. This model has two equilibrium points, that is disease-free equilibrium point which always exists and an endemic equilibrium point that exists with some conditions. The local stability of the equilibrium points is investigated by using Routh-Hurwitz criteria. The method of Next Generation Matrix is applied to get the basic reproduction number R0 . It can be shown numerically that disease-free equilibrium point is locally asymptotic stable when R0 < 1, while the endemic equilibrium point exist and locally asymptotic stable when satisfy Routh-Hurwitz criteria. Numerical simulations are given to illustrate the theoretical results.

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