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UID:9086@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260526T143000
DTEND;TZID=Europe/Paris:20260526T153000
DTSTAMP:20260522T172753Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-298/
SUMMARY:Yao Armand KANGA (Aix-Marseille Université): Spatial epidemic mode
 l with varying infectivity and waning immunity : Law of Large Numbers
DESCRIPTION:Yao Armand KANGA: Classical epidemic models often use ordinary 
 differential equations (ODEs)\, which assume implicitly exponential durati
 ons for infections\, and often an abrupt loss of immunity\, an unrealistic
  simplification. Recent research has explored models with more flexible di
 stributions for infection duration and waning of immunity. This work integ
 rates three key aspects:\n• Variable Infectivity: The infection transmis
 sion rate depends on the time elapsed since infection\, and differs from o
 ne individual to another\,\n• Waning immunity: Immunity acquired after r
 ecovery gradually decreases until full susceptibility is restored and diff
 ers from one individual to another\,\n• Spatial Structure: Individuals o
 ccupy distinct positions in space\, introducing heterogeneity in disease s
 pread. In this work\, we assume that the individuals do not move\,The infe
 ction rate depends on the respective positions of the individuals\, the cu
 rrent infectivity of\nthe 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 wi
 thin 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 infe
 ctious 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 infec
 tion\, $\\lambda(a_y (t))$ itsinfectivity\, $\\gamma(a_x(t))$ the suscepti
 bility of the individual undergoing infection\, and $K(x\, y)$ a kernel de
 pending on the positions x and y. We prove that the law of large numbers l
 imit of our finite population stochastic model\, as the size the populatio
 n tends to infinity is a set of integral equations parametrized by the spa
 tial position x.
CATEGORIES:Séminaire,ALEA,Probabilités
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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DTSTART:20260329T030000
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