The Study On A Class Of Models Of Biomathematics

The disease of bad breath has brought people distressed heavily in daily routines and activities. The mouth of a person is a complex ecosystem which is composed of more than700species of bacteria. It may cause the bad breath when pathogenic bacteria increase largely. The chemostat is most widely used in the practice of the model, and the model has played an important role in the economic, agricultural, biomedical science fields. In this paper, an oral microorganism Chemostat model under the background of bad breath has been considered. Then we analyze stability of the equilibrium points with practical significance.First, we obtain three dimensional equilibrium points and analyze stability of the equilibrium points with practical significance. We get the conclusion that the bad breath could not be cured by water gargle while medicine may successfully do it. In order to overcome the bad breath, the methods of impulse control have been imposed to the original system, and sufficient conditions of curing the disease have been received.Then, we consider the physiological way of human’s oral drug absorption. In the process of oral medication, there exists a decomposition process of drugs into the human body. Therefore in this paper we consider the mathematical model of the treatment time, and base on the analysis of the practical stability.At last there exists time delay in the process from absorbing nutrient to transforming the nutrition, which is the discrete time delay, so we build the chemostat model with the discrete time delay and cure the bad breath with the oral premedication. Because the concentration of the population at different moments will affect the growth rate of the population, we use the form of the integral weight to express the total effect for the past period of the time which brings the distributed time delay. We consider the chemostat model with the distributed time delay. Equilibrium points and their stability properties have been obtained with practical significance. Simulations results illustrate effectiveness of our results. Next we compare the model of with distributed time delay and without time delay, and we combine with practical significance for analysis.