  Different extensions of the classical single-strain SIR model for the host
population, motivated by modeling dengue fever epidemiology, have reported a
rich dynamic structure including deterministic chaos which was able to explain
the large fluctuations of disease incidences. A comparison between the basic
two-strain dengue model, which already captures differences between primary and
secondary infections, with the four-strain dengue model, that introduces the
idea of competition of multiple strains in dengue epidemics shows that the
difference between first and secondary infections drives the rich dynamics more
than the detailed number of strains to be considered in the model structure.
Chaotic dynamics were found to happen at the same parameter region of interest,
for both the two and the four-strain models, able to explain the fluctuations
observed in empirical data and showing a qualitatively good agreement between
empirical data and model simulation. Since the law of parsimony favors the
simplest of two competing models, the two-strain model would be the better
candidate to be analyzed, giving the expected complex behavior to explain the
fluctuations observed in empirical data, and indeed the better option for
estimating all initial conditions as well as the few model parameters based on
the available incidence data.
