Dynamics of a nonlocal diffusion virus model with age structure, heterogeneity, nonlinear incidence rates and time delays
Soufiane Bentout
Abstract
In this paper, we propose a comprehensive nonlinear model incorporating time delays and infection age to investigate the dynamics of virus cells within the human body. We establish the model’s well-posedness and identify the critical threshold represented by the basic reproduction number R0. Indeed, we show that when R0<1, the infection-free steady state E0 is globally asymptotically stable. Conversely, if R0>1, the model admits at least one endemic steady state that is globally asymptotically stable. Moreover, we complement our theoretical analysis with numerical simulations, which both illustrate and validate our mathematical results. The simulations demonstrate the model’s ability to capture the dynamics of free pathogens cells under various conditions, providing a valuable framework for understanding disease progression within the human body.