Effect of General Cross-Immunity Protection and Antibody- Dependent Enhancement in Dengue Dynamics
Abstract
A mathematical model to describe the dynamic of a multiserotype infectious disease at the population level is studied. Applied to
dengue fever epidemiology, we analyse a mathematical model with time delay to describe the cross-immunity protection period,
including a key parameter for the antibody-dependent enhancement (ADE) effect, the well-known features of dengue fever
infection. Numerical experiments are performed to show the stability of the coexistence equilibrium, which is completely
determined by the basic reproduction number and by the invasion reproduction number, as well as the bifurcation structures
for different scenarios of dengue fever transmission in a population. The model shows a rich dynamical behavior, from fixed
points and periodic oscillations up to chaotic behaviour with complex attractors.