**The classes originally scheduled for December 26 and January 2 are rescheduled to December 24 (Wednesday), from 9:00–12:00 and 14:00–17:00 (two consecutive sessions).

Dec. 24 session 1: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=mca7db3dadc068a91e8d537584a01ff42

Dec. 24 session 2: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=mde3d8894763644d4872e911fd1e9f51d

**Due to the year-end banquet on January 9, the class is rescheduled to January 7 (Wednesday) from 9:00–12:00.

Jan. 7: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m8ca2436d0884798f38764a834230e0ff

1. Introduction & Purposes

The proposed course is a 4-month topics course on An Introduction to Mathematical Epidemiology during my visit to NCTS. This course is specifically designed to lay a solid theoretical foundation in infectious disease modeling, with a focus on dynamical systems, bifurcation theory, stochastic processes, and networks. The course is intended for graduate students, senior undergraduates, and researchers interested in the mathematical underpinnings of infectious disease dynamics. Students will gain a comprehensive understanding of the mathematical tools necessary to model disease spread and analyze real-world epidemic data.

2. Outline & Descriptions

The course will be structured around a 3-hour lecture each week, providing in-depth theoretical insights and practical applications. Key topics include:

Venue: 清大綜三舘 Lecture room B onsite, 次震宇宙館 R. 509 broadcasting.

Week 1-2: Introduction to Epidemic Models– Overview of basic deterministic models(SIR, SEIR) with a focus on dynamical systems. Analysis of disease transmissiondynamics using ordinary differential equations and stability analysis.

Week 3-4: Bifurcation Theory and Critical Transitions– Study of bifurcation theory andhow it applies to the dynamics of disease models. Exploration of transitions betweendifferent epidemic states, such as disease elimination or endemic equilibrium, and therole of model parameters in these transitions.

Week 5-7: Stochastic Processes in Epidemiology– Introduction to stochastic models andrandom processes. Analysis of stochastic epidemic models, including Markov chainmodels and stochastic differential equation models, to capture variability in diseasespread and account for uncertainty.

Week 8-11: Network Theory and Epidemic Spreading– Application of network theory tomodel disease transmission across populations. Study of the role of social networks,mobility, and interactions in the spread of infectious diseases.

Week 12-13: Case Studies and Model Calibration– Application of the discussed modelsto real-world disease outbreaks (e.g., COVID-19, Cholera, influenza, Zika). Practicalsessions on model calibration, parameter estimation, and validation using actualepidemiological data.

Week 14-16: Interdisciplinary Applications– Integrating dynamical systems, bifurcationtheory, stochastic processes, and network theory to design more effective public healthstrategies. Emphasis on policy implications and decision-making in epidemic control.

3. Prerequisites

Dynamical Systems; Probability Theory

4. Online Meeting

Please contact Murphy <murphyyu@ncts.tw> if you need to participate online.

5. Registration

https://forms.gle/hUc753XAHCof393T7