Speaker 1: Dr. Louk-Man Issaka (Department of Mathematics, Universite Gaston Berger de Saint-Louis, Senegal)
Title 1: Stability for some impulsive neutral stochastic functional integro-differential equations driven by fractional Brownian motion
Abstract 1: The aim of this talk is to present the stability for some integro-differential equations driven by fractional Brownian motion with noncompact semigroup in Hilbert spaces. In this talk, we will assume that the linear part has a resolvent operator not necessarily compact, but is operator norm continuous. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Monch fixed point theorem. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.
Speaker 2: Dr. Alexis NANGUE
Title 2: Global dynamics of a spatiotemporal cellular model for the Hepatitis C virus infection with Hattaf-Yousfi functional response
Abstract 2: This work carries out a mathematical analysis of the global dynamics of a partial differential equation viral infection cellular model. We study the dynamics of a Hepatitis C virus (HCV) model, under therapy, that considers both absorption phenomenon and diffusion of virions, infected and uninfected cells in the liver. Firstly, we prove the boundedness of the potential solutions, global existence, uniqueness, and positivity of the solution to the obtained initial value and boundary problem. Then, the dynamical behaviour of the model is entirely determined by a threshold parameter called the basic reproduction number denoted R_0. We show that the HCV-uninfected spatially homogeneous equilibrium of the model is globally asymptotically stable if R_0 <= 1 by using the direct Lyapunov method. The latter means that the HCV infection is cleared, and the disease dies out. Also, the global asymptotic properties stability of the HCV-infected spatially homogeneous equilibrium of the model are studied via skillful construction of a suitable Lyapunov functional. It means that the HCV infection persists in the host, and the infection becomes chronic. Finally, numerical simulations are performed to support the theoretical results obtained.
Coordinator: Prof. Marc Sedjro (German Research Chair, AIMS South Africa)
Zoom Link: HERE
Meeting ID: 926 0538 0740
Passcode: 107706
Zoom Meeting Start Time: 2:45 pm (Accra Time)
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English