Prevalence-based modeling approach of schistosomiasis : global stability analysis and integrated control assessment

A system of nonlinear differential equations is proposed to assess the effects of prevalence-dependent disease contact rate, pathogen’s shedding rates, and treatment rate on the dynamics of schistosomiasis in a general setting. The decomposition techniques by Vidyasagar and the theory of monotone systems are the main ingredients to deal completely with the global asymptotic analysis of the system. Precisely, a threshold quantity for the analysis is derived and the existence of a unique endemic equilibrium is shown. Irrespective of the initial conditions, we prove that the solutions converge either to the disease-free equilibrium or to the endemic equilibrium, depending on whether the derived threshold quantity is less or greater than one. We assess the role of an integrated control strategy driven by human behavior changes through the incorporation of prevalence-dependent increasing the prophylactic treatment and decreasing the contact rate functions, as well as the mechanical water sanitation and the biological elimination of snails. Because schistosomiasis is endemic, the aim is to mitigate the endemic level of the disease. In this regard, we show both theoretically and numerically that: the reduction of contact rate through avoidance of contaminated water, the enhancement of prophylactic treatment, the water sanitation, and the removal of snails can reduce the endemic level and, to an ideal extent, drive schistosomiasis to elimination.The University of Pretoria Senior Postdoctoral Program Grant.https://www.springer.com/journal/403142022-01-20hj2021Mathematics and Applied Mathematic

Global analysis of a schistosomiasis infection model with biological control

International audienceIn this paper, the global stability of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mam-malian host and a competitor snail species is studied by constructing Lya-punov functions and using properties of K monotone systems. We derive the basic reproduction number R 0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R 0 . We show that the disease can be eradicated when R 0 ≤ 1. In the case where R 0 > 1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. This mathematical analysis of the model gives insight about the epidemiological consequences of the introduction of a competitor resistant snail species