First, I introduce the basic reproduction number of epidemic models. Then I talk about our studies on the basic reproduction numbers of periodic epidemic models and reaction-diffusion models, where the reproduction numbers are formulated, and the computational schemes are given. The influences of heterogeneity in time and space are also analyzed. The theoretical results are applied to rabies model and lyme disease model to reveal the control strategies for these infectious diseases. After that, I show you the mathematical analysis for stochastic model of
Alzheimer's disease. Analytical conditions for the stochastic P-bifurcation are derived by means of technique of slow-fast dynamical systems. A formula is presented to approximate the mean switching time from a normal state to a pathological state.

王稳地，西南大学数学与统计学院二级教授、博士生导师，中国生物数学学会副理事长，享受国务院特殊津贴，2005年获得重庆市名师称号, 2018年获得重庆市最美教师称号；主要从事生物数学和应用动力系统研究，在种群动力学和传染病动力学建模和分析方面发表论文100多篇，7次入选Elsevier数学类高引用论文作者;已经主持国家自然科学基金课题7项、教育部项目2项，是International Journal of Biomathematics和Journal of Biological systems等期刊编委。