Stochastic epidemic model with varying infectivity and waning immunity
Document Type
Lecture
Publication Date
4-17-2025
Abstract
After an individual has been infected by a pathogen, T lymphocytes store information about the pathogen. Consequently, upon reinfection by the same pathogen, an immune response memory is triggered. This immune memory allows the body to react very quickly against the pathogen. Indeed, when an individual recovers from a virus, sometimes the individual acquires full immunity. In some cases, the individual's immunity persists for some period, after which it decreases progressively and can even disappear. I will then present a stochastic epidemic model with memory on the previous infection, incorporating varying infectivity and waning immunity. More precisely, we will present a functional law of large numbers when the size of the population tends to infinity. We will also present results on the behavior of the epidemic, more precisely the threshold for the existence of an endemic equilibrium, and study the stability of the endemic equilibrium.
Relational Format
presentation
Recommended Citation
Zotsa, Brice, "Stochastic epidemic model with varying infectivity and waning immunity" (2025). Probability & Statistics Seminar. 70.
https://egrove.olemiss.edu/math_statistics/70
