Mathematical modeling in behavior responses: The tendency-prediction based on a persistence model on real-time data

Research on biological responses to water quality monitoring and toxicity prediction has increased in recognition in recent years. A great deal of biological response data has been produced through online monitoring systems. However, comprehensive information on biological response is missing. Consequently, biological responses cannot be used to monitor water quality. We can resolve this problem through mathematical models. We used the persistent model on behavioral strength data and derived a mathematic model. The threshold points for safe, acclimatization, adjustment and toxicity stages were calculated precisely. We obtained normal (Bn) and persistence (Bp) responses on behavior data when the environmental conditions of fish changed. Transfer of behavior strength from safe mode (Ms) to acclimatization mode (Mac) and Mac to adjustment stage (Maj) resulted rapidly; this indicates that fish sensed the environment changes. Serials of Maj stages were also visualized; hence, we determined upwards and downwards trends for each Maj. The toxicity stage (Mt) has occurred after the extended Maj stage, indicating that the toxic effect of the stressors overwhelmed the adaptive capability of the fish. We derived the threshold point for each stage precisely on the fish behavior strength dataset. Thus, the proposed mathematical model is an efficient model for determining the behavioral changes when toxicants enter an organism's body. Although the proposed mathematical model is derived using specific factors such as fishes, pollutants, and concentrations, it can be applicable for other biological models based on the normal and persistent responses for toxicity prediction. This study strengthens the available alternative environmental monitoring techniques towards water quality monitoring.