Abstract
Dengue is an epidemic disease rapidly spreading throughout many parts of the world, which is a serious public health concern. Understanding disease mechanisms through mathematical modeling is one of the most effective tools for this purpose. The aim of this manuscript is to develop and analyze a dynamical system of PDEs that describes the secondary infection caused by DENV, considering (i) the diffusion due to spatial mobility of cells and DENV particles, (ii) the interactions between multiple target cells, DENV, and antibodies of two types (heterologous and homologous). Global existence, positivity, and boundedness are proved for the system with homogeneous Neumann boundary conditions. Three threshold parameters are computed to characterize the existence and stability conditions of the model's four steady states. Via means of Lyapunov functional, the global stability of all steady states is carried out. Our results show that the uninfected steady state is globally asymptotically stable if the basic reproduction number is less than or equal to unity, which leads to the disappearance of the disease from the body. When the basic reproduction number is greater than unity, the disease persists in the body with an active or inactive immune antibody response. To demonstrate such theoretical results, numerical simulations are presented.