Évènement

Yao Armand KANGA
Aix-Marseille Université

Date(s) : 26/05/2026   iCal
14h30 - 15h30

Classical epidemic models often use ordinary differential equations (ODEs), which assume implicitly exponential durations for infections, and often an abrupt loss of immunity, an unrealistic simplification. Recent research has explored models with more flexible distributions for infection duration and waning of immunity. This work integrates three key aspects:
• Variable Infectivity: The infection transmission rate depends on the time elapsed since infection, and differs from one individual to another,
• Waning immunity: Immunity acquired after recovery gradually decreases until full susceptibility is restored and differs from one individual to another,
• Spatial Structure: Individuals occupy distinct positions in space, introducing heterogeneity in disease spread. In this work, we assume that the individuals do not move,The infection rate depends on the respective positions of the individuals, the current infectivity of
the infectious individuals and the susceptibility of the target individual. In our work, we explore the spread of infectious diseases in epidemic model with varying infectivity and waning immunity within a spatially structured population. Individuals are distributed over a subset $D ⊂ \mathbb{R}^d$. We consider a population of fixed size N on D; and we assume that, at the initial time, the population is divided into two subsets: infected and uninfected . In the simplest version of our model, the infection of a susceptible individual located at x by an infectious individual located at y occurs at a rate $\gamma(a_x(t))K(x, y) \lambda(a_y (t))$ , where $a_{\cdot}(t)$ is the time elapsed since infection, $\lambda(a_y (t))$ itsinfectivity, $\gamma(a_x(t))$ the susceptibility of the individual undergoing infection, and $K(x, y)$ a kernel depending on the positions x and y. We prove that the law of large numbers limit of our finite population stochastic model, as the size the population tends to infinity is a set of integral equations parametrized by the spatial position x.

Emplacement
I2M Saint-Charles - Salle de séminaire

Catégories

• Séminaire