title: Stochastic dynamics of dengue epidemics.
abstract: We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of 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, for any death rate of infected mosquitoes.
authors: Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, Brazil.
authors: David R
authors: DR
authors: de Souza
authors: Tânia
authors: T
authors: Tomé
authors: Suani T R
authors: ST
authors: Pinho
authors: Florisneide R
authors: FR
authors: Barreto
authors: Mário J
authors: MJ
authors: de Oliveira
mesh_terms: D000330:Aedes; D000818:Animals; D003198:Computer Simulation; D009033:Culicidae / Q000821:virology*; D003715:Dengue / Q000453:epidemiology* / Q000635:transmission*; D003716:Dengue Virus; D004196:Disease Outbreaks; D004198:Disease Susceptibility / Q000453:epidemiology; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D007303:Insect Vectors / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical; D013269:Stochastic Processes