  Vector-transmitted diseases such as dengue fever and chikungunya have been
spreading rapidly in many parts of the world. The Zika virus has been known
since 1947 and invaded South America in 2013. It can be transmitted not only by
(mosquito) vectors but also directly through sexual contact. Zika has developed
into a serious global health problem because, while most cases are asymptomatic
or very light, babies born to Zika - infected mothers may develop microcephaly
and other very serious birth defects.
  We formulate and analyze two epidemic models for vector-transmitted diseases,
one appropriate for dengue and chikungunya fever outbreaks and one that
includes direct transmission appropriate for Zika virus outbreaks. This is
especially important because the Zika virus is the first example of a disease
that can be spread both indirectly through a vector and directly (through
sexual contact). In both cases, we obtain expressions for the basic
reproduction number and show how to use the initial exponential growth rate to
estimate the basic reproduction number. However, for the model that includes
direct transmission some additional data would be needed to identify the
fraction of cases transmitted directly. Data for the 2015 Zika virus outbreak
in Barranquilla, Colombia has been used to fit parameters to the model
developed here and to estimate the basic reproduction number.
