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One of the modern, recently developed mathematical approaches for modeling various complex chaotic processes (the bacteria migration is apparently one of them), is the application of fractional differential equations. Introduction of fractional derivatives is also a very effective approach for investigation of the reactive processes (growth of bacteria in our case). Our recent advances in application of fractional differential equations for modeling the anomalous transport of reactive and non-reactive contaminants (see our recent publications in the References) allow us to expect that the anomalous transport of growing bacteria can also be effectively described by the models with fractional derivatives. Based on these modern approaches, utilizing fractional differential equations, in this paper we developed a reliable mathematical model that could be properly calibrated and, consequently, provide an adequate description of the growing bacteria transport. This model accounts for the memory effects in the bacteria transport due to the random character of bacteria trapping and release by the porous matrix. Two types of bacteria in the saturated porous medium are considered: mobile and immobile bacteria. Bacteria in the mobile phase are migrating in the fluid and have the velocity of the bulk flow, whereas bacteria in the immobile phase are the bacteria that are captured by the porous matrix. These bacteria have zero velocity and can cause clogging of some pores (therefore, porosity is possibly not constant). Examining different conventional models and comparing computations based on these models, we show that this extremely complex character of bacteria transport cannot be described by the traditional approach based on classical partial differential equations. In this paper we suggest fractional differential equations as a simple but very effective tool that can be used for constructing the proper model capable of simulating all the above-mentioned effects associated with migration of alive bacteria. Using this approach, a reliable model of the growing bacteria transport in the porous medium is developed and validated by comparison with experimental laboratory results. We proved that this novel model can be properly linearized and calibrated, so that an excellent agreement with available experimental results can be achieved. This simple model can be used in many applications, for example, as a part of more general mathematical models for predicting the outcomes of the bioremediation of contaminated soils. [ABSTRACT FROM AUTHOR]

One of the modern, recently developed mathematical approaches for modeling various complex chaotic processes (the bacteria migration is apparently one of them), is the application of fractional differential equations. Introduction of fractional derivatives is also a very effective approach for investigation of the reactive processes (growth of bacteria in our case). Our recent advances in application of fractional differential equations for modeling the anomalous transport of reactive and non-reactive contaminants (see our recent publications in the References) allow us to expect that the anomalous transport of growing bacteria can also be effectively described by the models with fractional derivatives. Based on these modern approaches, utilizing fractional differential equations, in this paper we developed a reliable mathematical model that could be properly calibrated and, consequently, provide an adequate description of the growing bacteria transport. This model accounts for the memory effects in the bacteria transport due to the random character of bacteria trapping and release by the porous matrix. Two types of bacteria in the saturated porous medium are considered: mobile and immobile bacteria. Bacteria in the mobile phase are migrating in the fluid and have the velocity of the bulk flow, whereas bacteria in the immobile phase are the bacteria that are captured by the porous matrix. These bacteria have zero velocity and can cause clogging of some pores (therefore, porosity is possibly not constant). Examining different conventional models and comparing computations based on these models, we show that this extremely complex character of bacteria transport cannot be described by the traditional approach based on classical partial differential equations. In this paper we suggest fractional differential equations as a simple but very effective tool that can be used for constructing the proper model capable of simulating all the above-mentioned effects associated with migration of alive bacteria. Using this approach, a reliable model of the growing bacteria transport in the porous medium is developed and validated by comparison with experimental laboratory results. We proved that this novel model can be properly linearized and calibrated, so that an excellent agreement with available experimental results can be achieved. This simple model can be used in many applications, for example, as a part of more general mathematical models for predicting the outcomes of the bioremediation of contaminated soils.

We purpose in this study to develop a reliable and low-cost method for the detection of Viable but nonculturable (VBNC) bacteria. Indeed, after water disinfection, injured-VBNC bacteria can be underestimated using conventional assessment methods, causing false-negative results and, posing a significant and potential health risk. The VBNC bacterial survival strategy can hide the real microbial quality of treated water. To overcome this bacterial assessment limitation, we were used a specific and lytic phage to monitor the presence of active bacteria; Pseudomonas aeruginosa after photocatalytic treatment. Within 2 h of phage-target bacteria contact, the reduction of phage amplification rate (At) can reveal the ability of specific-lytic phage to recognize and to attach to their host cells with a probability of new infectious phages release despite their lose of cultivability in the usual media. The determination of phage reactivation coefficient (Rt) after 2 and 8 h of phage-target cell contact time reveals the ability of phages to reactive their infectivity and their amplification in positive correlation with their host cells viability and activity. The increase in phage reactivation coefficient (Rt) after an extension of the latent period was directly related to the positive interaction between infectious phages and potential active bacteria. The use of this method can improve the water disinfection process and avoid public health-hazardous especially related to the resuscitation of active-nonculturable bacteria mainly for pathogenic bacteria. [ABSTRACT FROM AUTHOR]