Abstract
During the past eras, many mathematicians have paid their attentions to model the dynamics of dengue virus (DENV) infection but without taking into account the mobility of the cells and DENV particles. In this study, we develop and investigate a partial differential equations (PDEs) model that describes the dynamics of secondary DENV infection taking into account the spatial mobility of DENV particles and cells. The model includes five nonlinear PDEs describing the interaction among the target cells, DENV-infected cells, DENV particles, heterologous antibodies, and homologous antibodies. In the beginning, the well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive three threshold parameters which govern the existence and stability of the four equilibria of the model. We study the global stability of all equilibria based on the construction of suitable Lyapunov functions and usage of Lyapunov–LaSalle’s invariance principle (LLIP). Last, numerical simulations are carried out in order to verify the validity of our theoretical results.