In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions.

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A literature review of metal mixture interaction analyses identified that there was not a consistent method to determine the impact of metal mixtures on an aquatic organism. The review also revealed that a majority of the research on mixtures made use of water concentrations only. Therefore research was conducted to determine the relationship between exposure, bioaccumulation and chronic effects of the four elements As, Co, Cr and Mn individually. Mechanistically based saturation models of bioaccumulation and toxicity were determined for the benthic invertebrate Hyalella azteca, from which lethal water concentrations and body concentrations were also determined. These models were then combined with those previously done for the metals Cd, Cu, Ni, Pb, Tl and Zn to model the impact of 10 metal mixtures on bioaccumulation in short term (1-week) exposures and on bioaccumulation and toxicity in chronic (4-week) exposures at “equi-toxic” concentrations. Interactions between the metals were identified in which; Cd, Co and Ni bioaccumulations were significantly inhibited, Tl and Zn bioaccumulations were marginally inhibited, there was no impact on Cr, Cu or Mn bioaccumulation, and both As and Pb bioaccumulation were enhanced by some mixtures of metals. It was determined that strict competitive inhibition may be a plausible mechanism of interaction affecting Co, Cd and Ni bioaccumulation but not for any of the other metals. However, it is possible that other interactions such as non-competitive or anti-competitive inhibition may have been responsible. A metal effects addition model (MEAM) was developed for Hyalella azteca based on both the bioaccumulation (body concentrations) to effects and the exposure (water concentration) to effects relationships developed from the single metal only studies The MEAM was used to predict the impact of metal mixture exposures on mortality. Toxicity was under-estimated when based on measured water or body concentrations, however, its best prediction was based on body concentrations. The MEAM, when based on measured body concentrations, takes bioavailability into account, which is important since the chemical characteristics of water can greatly alter the bioavailability and therefore toxicity of metals. The MEAM was compared to the traditional Concentration Addition Model (CAM), which calculates toxic units based on water concentrations and LC50s or body concentrations and LBC50s. The CAM overestimated toxicity, but had its best prediction when based on water concentrations. Over all, the best fit to observed mortality was the prediction by the MEAM, based on body concentrations. The measurement of bioaccumulated metals and the use of the MEAM could be important in field site assessments since it takes into account changes in bioavailability due to different site water chemistries whereas the traditional CAM based on water concentration does not.

A literature review of metal mixture interaction analyses identified that there was not a consistent method to determine the impact of metal mixtures on an aquatic organism. The review also revealed that a majority of the research on mixtures made use of water concentrations only. Therefore research was conducted to determine the relationship between exposure, bioaccumulation and chronic effects of the four elements As, Co, Cr and Mn individually. Mechanistically based saturation models of bioaccumulation and toxicity were determined for the benthic invertebrate Hyalella azteca, from which lethal water concentrations and body concentrations were also determined. These models were then combined with those previously done for the metals Cd, Cu, Ni, Pb, Tl and Zn to model the impact of 10 metal mixtures on bioaccumulation in short term (1-week) exposures and on bioaccumulation and toxicity in chronic (4-week) exposures at “equi-toxic” concentrations. Interactions between the metals were identified in which; Cd, Co and Ni bioaccumulations were significantly inhibited, Tl and Zn bioaccumulations were marginally inhibited, there was no impact on Cr, Cu or Mn bioaccumulation, and both As and Pb bioaccumulation were enhanced by some mixtures of metals. It was determined that strict competitive inhibition may be a plausible mechanism of interaction affecting Co, Cd and Ni bioaccumulation but not for any of the other metals. However, it is possible that other interactions such as non-competitive or anti-competitive inhibition may have been responsible. A metal effects addition model (MEAM) was developed for Hyalella azteca based on both the bioaccumulation (body concentrations) to effects and the exposure (water concentration) to effects relationships developed from the single metal only studies The MEAM was used to predict the impact of metal mixture exposures on mortality. Toxicity was under-estimated when based on measured water or body concentrations, however, its best prediction was based on body concentrations. The MEAM, when based on measured body concentrations, takes bioavailability into account, which is important since the chemical characteristics of water can greatly alter the bioavailability and therefore toxicity of metals. The MEAM was compared to the traditional Concentration Addition Model (CAM), which calculates toxic units based on water concentrations and LC50s or body concentrations and LBC50s. The CAM overestimated toxicity, but had its best prediction when based on water concentrations. Over all, the best fit to observed mortality was the prediction by the MEAM, based on body concentrations. The measurement of bioaccumulated metals and the use of the MEAM could be important in field site assessments since it takes into account changes in bioavailability due to different site water chemistries whereas the traditional CAM based on water concentration does not.