Date/Time Date(s) - 02/04/202610:30 am - 11:30 am
Title: Math Bio Graduate Seminar
Location: Hamilton Hall, Room 410 & Zoom Zoom link: https://mcmaster.zoom.us/j/98308755554 (Passcode: MathBio)
Speaker: Runtian Zhou Title: Pandemic Bond Pricing under Trigger Rules: Comparing Stochastic Logistic Growth and SIRD Epidemic Models. Abstract: In this project, I start from a stochastic logistic growth framework for modeling epidemic dynamics, and then extend it by embedding a SIRD model into the epidemic component. This allows me to better capture the evolution of infections, recoveries, and deaths, which are directly linked to the bond’s trigger conditions. Using these models, I simulate trigger events and evaluate how they affect payout probabilities and the resulting pandemic bond pricing.
Speaker: Emma Coates Abstract: Mechanistic models like the Susceptible-Infected-Recovered (SIR) model are widely used to study recurrent childhood infectious disease epidemics, where a key mechanism for reproducing these recurrent epidemics is seasonal variation in contact rates, often represented either as a smooth sine wave or as “term-time forcing” tied to school calendars. A key question is to what extent does it matter that a simple sinusoidal model or a true term-time seasonal model is used in modelling epidemic transitions. Building on prior work by Papst and Earn, this talk presents an extended framework showing that epidemic predictions remain consistent across different seasonal structures for both transient and long-term epidemic dynamics, suggesting that transient behaviour may help explain observed frequency shifts in diseases like whooping cough.
Speaker:Ning Yu Abstract: In this talk, I will present a mathematical model for the transmission of louping ill in a tick–red grouse system. The model includes three transmission routes: biting transmission, co-feeding transmission between ticks on the same host, and predation-mediated transmission when red grouse chicks ingest infected ticks. It also takes into account both tick life stages and the age structure of red grouse. Using this framework, I study threshold dynamics for tick persistence and disease invasion, and show how these thresholds determine whether the system approaches a tick-free state, a disease-free state, or an endemic equilibrium. I will also discuss the biological implications of the analysis. In particular, the results show that co-feeding can play an important role in sustaining transmission, while sufficiently strong predation can prevent long-term persistence of the disease. The model also reveals that predation on adult ticks may have a non-monotone effect, so that intermediate predation levels can sometimes be most favorable for outbreaks. When disease-induced mortality in red grouse is included, the system can exhibit more complicated dynamics, including oscillations and bistability. Overall, this work helps clarify how co-feeding and predation interact in louping ill transmission and may offer useful insight for disease control and red grouse management.