Study On Two Types Of Stochastic Models Of Biological Mathematics

In recent years,Stochastic differential equations(SDES)have been developed rapidly and widely used in various fields,especially in biological mathematics.In this paper,two types of stochastic biomathematical models,namely COVID-19 infectious disease model and population ecological model,are constructed,and the survival analysis of the models is carried out by using stochastic differential equation theory,Ito formula and Lyapunov function.In the first chapter,we mainly introduce the research background and significance of the paper,and briefly analyze the application and development of stochastic differential equations in the field of biomathematics.In Chapter 2,we give the necessary theoretical knowledge for the paper.In Chapter 3,we establish a novel stochastic mathmatical model for COVID-19 with tracking and quarantine,and obtains sufficient conditions for the existence of the stationary distribution and extinction of neocrown pneumonia by constructing a suitable Lyapunov function.In Chapter 4,we mainly study a kind of stochastic population competition model with time delay in polluted environment.By using the Ito formula and related theories,we obtain the sufficient conditions of two species extinction,non-average persistence,weak average persistence and strong average persistence,and analyze the thresholds for survival of extinction and weak average persistence.The fifth chapter summarizes the paper,reflects on the shortcomings,and makes prospects for future research.