Section: New Results

Bilharzia

Schistosomiasis or bilharzia is a water-borne parasitic disease that affects 200 million people and poses a treat to 600 million in more than 76 countries [39] . It is caused by blood-dwelling fluke worms of the genus Schistosoma. The transmission cycle requires contamination of surface water by excreta, specific freshwater snails as intermediate hosts, and human water contact [21] . Schistosome are transmitted via contact with contaminated water containing cercaria the infective stage of the parasite [39] , [32] .

In connection with EPLS, a research NGO based in Saint-Louis (Senegal), and Pasteur Institute of Lille, we investigate a spatially deterministic metapopulation model in which infectious agents persist within a network of connected environments. This model accounts for human population age and behavior structure. We completely analyses the asymptotic behavior of this model. We give a formula for computing the basic reproduction ratio ${ℛ}_0$. If ${ℛ}_0\le 1$ we prove that the disease free equilibrium is globally asymptotically stable. If ${ℛ}_0>1$, with an hypothesis on connectedness, we prove that there exists a unique positive endemic equilibrium, which is globally asymptotically stable.

The validation of this model, using data of EPLS, is under investigation and is the subject of a Phd thesis. The defense will occur at the beginning of 2013. We explore the identification of key parameters using different kind of observers.

Figure 1. Noisy and discrete measure of host prevalence

Figure 2. Reconstruction of the snail prevalence from preceding data