| Abstract: |
| In this presentation, I will discuss two commonly employed techniques for the theoretical analysis of stochastic differential equation (SDE) systems that frequently arise in the modeling of biological and medical problems. The first technique involves constructing Lyapunov functions to establish the existence of a unique stationary distribution of a SDE system within its invariant domain. The second technique involves studying the dynamics of a SDE system on the boundary of its invariant domain. This latter method offers several advantages and can yield precise conditions for both the persistence and extinction of a SDE system, which is of significant interest in the field of mathematical biology. To illustrate the integration of these techniques, I will utilize the cholera epidemic model and the human papillomavirus model. |
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