# Mohamed El Khalifi: Extending SIRS epidemics to allow for gradual waning of immunity

**Time: **
Wed 2023-02-15 15.15 - 16.00

**Location: **
Cramér room, Albano

**Participating: **
Mohamed El Khalifi, Stockholm University

### Abstract

The SIRS epidemic model for the spreading of infectious diseases makes the extreme assumption that individual immunity drops all at once. Here, a novel mathematical model is presented allowing for gradual waning of immunity following linear or exponential waning modes. The two new models and the SIRS model are compared assuming all three models have the same cumulative immunity. When no intervention is put in place, we find that the long-term prevalence is higher for the models with gradual waning. If aiming for herd immunity by continuous vaccination, it is shown that larger vaccine quantities are required when immunity wanes gradually compared with results obtained from the SIRS model, and this difference is biggest for the most realistic assumption of exponentially waning of immunity.