Claudia Pio Ferreira
Dengue hemorrhagic fever from a mathematical point of view
We will discuss some mathematical models that have been used to simulate the dynamics of the interaction among dengue virus, target cells, and immunological cells in the context of dengue hemorrhagic fever (DHF). In particular, we will focus on the hypothesis that postulates that cross-reactive antibodies are responsible for the enhancement of the infection in a phenomenon called antibody-dependent enhancement. The proposed models reproduce the dynamic of susceptible and infected target cells and dengue virus in scenarios of infection-neutralizing and infection-enhancing antibodies. The enhancement and neutralization functions are derived from basic concepts of chemical reactions. Following the traditional study of dynamics systems, we will present the equilibrium points, the stability analysis, the threshold parameter, temporal dynamics of the cells and antibodies populations, and global sensitivity analysis. The interpretation of the mathematical results will be transferred to the context of immunology to address the role of the antibodies’ response in the dengue-virus infection course.