- Sponsor
- Department of Mathematics
- Speaker
- Guodong Pang (Rice University)
- Contact
- Xuan Wu
- Originating Calendar
- Mathematics Seminar Series: Probability
Title: Recent advances in stochastic epidemic models.
Abstract: In this talk, I will give an overview of the recent advances in individual-based stochastic epidemic models and their large population approximations. We will discuss both homogeneous and nonhomogeneous populations, together with realistic individual infection, recovery, and immunity profiles. Individuals may be associated with a random, varying infectivity function and a random waning-immunity function. For homogeneous populations with infection-age-dependent infectivity, PDE and SPDE models are derived to approximate the dynamics of epidemic evolution. To capture heterogeneity among individuals and their connectivity, an individual-based epidemic model on large-scale inhomogeneous random graphs is developed, yielding a PDE on a graphon as an approximation to its dynamics. We will discuss spatial epidemic models with such individual infection profiles and their approximations via PDEs on a graphon. Some open problems will also be discussed.