  An epidemic multi-strain model with temporary cross-immunity shows chaos,
even in a previously unexpected parameter region. Especially dengue fever
models with strong enhanced infectivity on secondary infection have previously
shown deterministic chaos motivated by experimental findings of
antibody-dependent-enhancement (ADE). Including temporary cross-immunity in
such models, which is common knowledge among field researchers in dengue, we
find a deterministically chaotic attractor in the more realistic parameter
region of reduced infectivity on secondary infection (''inverse ADE'' parameter
region). This is realistic for dengue fever since on second infection people
are more likely to be hospitalized, hence do not contribute to the force of
infection as much as people with first infection.
  Our finding has wider implications beyond dengue in any multi-strain
epidemiological systems with altered infectivity upon secondary infection,
since we can relax the condition of rather high infectivity on secondary
infection previously required for deterministic chaos. For dengue the finding
of wide ranges of chaotic attractors open new ways to analysis of existing data
sets.
