Establishment And Analysis Of Two Classes Of Biokinetic Models

In this paper,two classes of biokinetic models are established and analyzed,one type of model is studied from the population level,and the other type of model is based on protein molecular level.First,a three-species predator-prey model with two time delays and Holling type-II functional response was analyzed.The stability of model at positive equilibrium point and the existence of Hopf bifurcation were discussed.The equilibrium point was taken as the research object,and characteristic equation of the system was analyzed.When the delay was equal to zero,the asymptotic stability condition at positive equilibrium point was obtained according to Hurwitz criterion.When the delay existed,the stability of the system was judged at the positive equilibrium point according to Bulter lemma.Taking two time delays as Hopf bifurcation parameters,the critical value of the system existing Hopf bifurcation at the positive equilibrium point was obtained.When the delay was greater than the critical value and the periodic solution existed,the model is numerically simulated by taking appropriate parameters and different time delay values,and diagrams of every component changes and solution curves are given around of critical value.The results show that with the variation of branch parameters,not only the stability of the system will change,but also produces Hopf bifurcation.Secondly,with the constant discovery of anti-cardiovascular autoantibodies and its mech-anisms,the function of autoimmune mechanism in development of hypertension has aroused people's attention.In particular,the study of ?1-Adrenergic receptor(?1-AR)autoantibod-ies(?1-AA)has become one of the hottest topics in recent research.In this paper,dy-namical models are constructed to discuss molecular mechanism of Agonistic autoantibodies(?1-AA)induce a1-Adrenergic receptor(?1-AR)non-desensitization.On the one hand,ac-cording to predecessor's researches,we can know that endocytosis dysfunction and confor-mation changes are possible molecular mechanisms.On the other hand,we further confirm that compound model of multiple mechanisms is the most likely model by comparing the fitting rates,analysing simulated and predicted images and contrasting Bayesian information criterions(BIC's).Because the BIC'S of compound model of multiple mechanisms and con-formation changes are quite close,it can be concluded that conformation changes is the main molecular mechanism.Based on the results of previous study,a model was again established by taking into account the normal physiological response of the healthy body.By analyzing the positive equilibrium point of the model,we can obtain that reducing the concentration of B1C(complex of ?1-AR binding to ?1-AA)can treat hypertension to a certain extent.Some treatment measures are suggested,such as injecting Adrenaline or reducing concentration of?1-AR and ?1-AA to prevent the deterioration of hypertension as much as possible.