title: Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue.
abstract: A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by R, is less than 1, the disease does not invade the populations and when R is greater than 1 it does. By not invading the population we mean that the number of infected individuals always decrease in subsequent seasons of transmission. Using the same threshold, all the qualitative features of the resulting epidemic can be understood. Our model suggests that trans-ovarial infection in the mosquitoes facilitates dengue overwintering. We also explain the delay between the peak in the mosquitoes population and the peak in dengue cases.
authors.affiliation: School of Medicine, The University of São Paulo and LIM 01/HCFMUSP, Av. Dr. Arnaldo 455, São Paulo, CEP 01246-903, SP, Brazil.
authors.forename: F A B
authors.initials: FA
authors.lastname: Coutinho
authors.forename: M N
authors.initials: MN
authors.lastname: Burattini
authors.forename: L F
authors.initials: LF
authors.lastname: Lopez
authors.forename: E
authors.initials: E
authors.lastname: Massad
mesh_terms: D000330:Aedes / Q000254:growth & development* / Q000821:virology; D000818:Animals; D001938:Brazil / Q000453:epidemiology; D003198:Computer Simulation; D003715:Dengue / Q000453:epidemiology / Q000635:transmission* / Q000821:virology; D003716:Dengue Virus / Q000254:growth & development; D004196:Disease Outbreaks; D005260:Female; D006801:Humans; D007303:Insect Vectors / Q000254:growth & development* / Q000821:virology; D008954:Models, Biological; D012621:Seasons