Orateur
Description
We study an individual-based stochastic host–vector epidemic model for malaria, in which humans can experience repeated infections over their lifetime. In contrast to classical Ross–Macdonald or compartmental SIR/SEIR models, each infection episode is characterised by a random time-dependent infectivity profile: after infection, a human host transmits parasites to susceptible mosquitoes according to a random infectivity function of the time since infection, while recovered hosts gradually regain susceptibility according to a random susceptibility function. On the vector side, susceptible mosquitoes become infected through contact with infectious humans and then contribute to transmission until death, under a demographic regime that combines birth and mortality processes.
We analyse the large-population asymptotic behaviour of this coupled host–vector system and prove a functional law of large numbers (FLLN) by constructing a sequence of i.i.d. auxiliary processes. The limiting dynamics are described by a nonlinear deterministic system of renewal-type integral equations that generalises both the classical Kermack–McKendrick age-of-infection framework and standard malaria models. In this limit, the solution of the limiting deterministic system depends on the expectation of a complicated functional of the random susceptibility functions, but only on the mean infectivity functions of humans and mosquitoes.
Othmane Baghdadi¹ and Étienne Pardoux²
¹ Mohammed First University, Oujda, Morocco — othmane.baghdadi.d23@ump.ac.ma
² Aix-Marseille University, CNRS, I2M, 13453 Marseille, France — etienne.pardoux@univ-amu.fr