  Dengue and Zika incidence data and the latest research have raised questions
about how dengue vaccine strategies might be impacted by the emergence of Zika
virus. Existing antibodies to one virus might temporarily protect or promote
infection by the other through antibody-dependent enhancement (ADE). With this
condition, understanding the dynamics of propagation of these two viruses is of
great importance when implementing vaccines. In this work, we analyze the
effect of vaccination against one strain, in a two-strain model that accounts
for cross-immunity and ADE. Using basic and invasion reproductive numbers, we
examined the dynamics of the model and provide conditions to ensure the
stability of the disease-free equilibrium. We provide conditions on
cross-immunity, ADE and vaccination rate under which the vaccination could
ensure the global stability of the disease-free equilibrium. The results
indicate scenarios in which vaccination against one strain may improve or
worsen the control of the other, as well as contribute to the eradication or
persistence of one or both viruses in the population.
