Analyse mathématique de modèles structurés de maladies hydriques: application au Laos

Abstract

In this thesis, we introduced an innovative model that integrates spatial interactions between humans and snails, along with an in-depth analysis of the prevalence of schistosomiasis in humans. Our primary objective is to demonstrate the existence of a monotone wave of propagation linking an unstable endemic equilibrium to a stable disease-free equilibrium. The results show that for schistosomiasis to spread, the propagation speed of the disease must exceed that of the water flow. Next, we focus on coupling the schistosomiasis model with the Saint-Venant equation. We establish the well-posedness and positivity of the solution. Our observations reveal that the speed of the water has a greater influence on the situation than depth. In low-flow areas, shallow depth contributes to the concentration of schistosomiasis by creating favorable conditions for snails and the survival of the parasite. In the final chapter, we develop a compartmental model that takes into account the life cycle of the schistosome and three types of definitive hosts: humans, carabaos, and rodents, to describe the situation in Lake Mainit. The main objective is to determine the optimal control strategy to reduce the prevalence of schistosomiasis. The study demonstrates that mechanical and aquatic controls, while beneficial, are insufficient on their own to interrupt transmission. We recommend a comprehensive and integrated control strategy that combines chemotherapy, mechanical measures, and aquatic interventions.