A nonautonomous dynamical system applied to dengue seasonality

Abstract

Seasonality due to environmental influences often affects contact between species for food or shelter as well as the spread and persistence of diseases from those vector species. Epidemic models may capture seasonality patterns in a phenomenological way by making the epidemiological parameters and the population demographics are time-periodic. A mathematical model with these features for the dengue fever is analyzed, to such an extent that the threshold between uniform persistence and extinction of the disease is established, that is: there exists a unique positive disease-free periodic solution being globally asymptotically stable when the basic reproductive number is greater that one, but it is unstable when the basic reproductive number is less than one, in whose situation there exists at least one non-trivial positive periodic solution and dengue fever is endemic in the community. At last, numerical simulations are carried out to illustrate the theoretical results.

Keywords

• aedes aegypti and dengue
• seasonality
• periodic system
• stability
• extinction
• persistence