Speaker: Dr. Burcu Gürbüz (Institute of Mathematics, Johannes Gutenberg-University Mainz)

Title: Dynamics of disease transmission models incorporating environmental viral concentration and vaccination effects 

Abstract: In this talk, we explore a mathematical model of disease transmission that incorporates two critical factors: imperfect vaccination coverage and infection from environmental viral particles. Motivated by the COVID-19 pandemic and debates about non-pharmaceutical interventions, this model provides a framework for understanding the combined effects of vaccination and environmental transmission pathways. A distinctive feature of the model is the inclusion of a response function, parameterized by an integer \( n \geq 1 \), which characterizes how environmental viral concentrations influence transmission dynamics. Through analytical and numerical analysis, we reveal the occurrence of backward bifurcations, where an endemic equilibrium persists even when the basic reproduction number \( R_0 \) is less than one. In addition, we demonstrate the existence of multiple endemic equilibria under certain parameter regimes. The study also considers extensions of the model that incorporate the effects of climate change, providing a broader perspective on how environmental factors shape disease dynamics. This analysis highlights the interplay between vaccine efficacy, environmental contributions to transmission, and potential shifts driven by changing ecological conditions, providing valuable insights for public health strategies.