Survival Analysis Of Single Population Model In The Polluted Environment

In real life, environmental pollution problem is more and more attended, if not pollutants control timely, but also severely affects the survival of populations, even endangers human health directly or indirectly. People often control emissions of pollutants or extend the period of the emission of pollutants to ensure the safe living environment of population. Three kinds of single species model in the polluted environment have been studied and the dynamics behavior of the models has been analyzed in this paper. Main research contents are as follows:Taking into account the impact of environmental pollution on human health, the mathematical model with the food chain in a polluted environment is established.Using the Comparison Principle, the all solutions of model are bounded. By Stability Analysis, we prove the global stability of the equilibrium of model. The model is applied to the study of residents eating fish containing mercury, and estimate the value of parameters of the model based on the existing data, calculate the safe range of residents eating fish containing mercury, then the maximum safe use amount of residents eating fish containing mercury is got.Considering the condition of the toxins pulse input to a small environment, the intrinsic rate of population is affected by environment and toxin in organisms which is influenced by toxin in the environment and the food chain. A new mathematical model is derived. Using the Comparison Principle, we prove that the all solutions of model are bounded. By the Pulse Compare Theorem, the surviving threshold of the population is found and the sufficient conditions of persistence and extinction of the population are obtained. Numerical simulation using MATLAB verifies correctness of the conclusions, and the effects of the rate of toxins input and the cycle of toxins input on the population are analyzed.Considering the populations have different physiological conditions in different stages, they are divided into two stages--immature and mature, and the model of a single-species population model with stage structure and pulse toxicant input in asmall polluted environment is studied. By Theoretical Differential Equations, the conditions of persistence and extinction of the population are obtained. Numerical simulation using MATLAB verifies correctness of the conclusions, and the effects of the time of population growing from the immature to mature, the rate of toxins input and the cycle of toxins input on the population are analyzed.