  We use a stochastic Markovian dynamics approach to describe the spreading of
vector-transmitted diseases, like dengue, and the threshold of the disease. The
coexistence space is composed by two structures representing the human and
mosquito populations. The human population follows a
susceptible-infected-recovered (SIR) type dynamics and the mosquito population
follows a susceptible-infected-susceptible (SIS) type dynamics. The human
infection is caused by infected mosquitoes and vice-versa so that the SIS and
SIR dynamics are interconnected. We develop a truncation scheme to solve the
evolution equations from which we get the threshold of the disease and the
reproductive ratio. The threshold of the disease is also obtained by performing
numerical simulations. We found that for certain values of the infection rates
the spreading of the disease is impossible whatever is the death rate of
infected mosquito.
