Complex behaviour in a dengue model with a seasonally varying vector population

• Published in: Mathematical biosciences 2014-02, Vol.248, p.22-30
• Main Authors: McLennan-Smith, Timothy A., Mercer, Geoffry N.
• Format: Article
• Language: English
• Subjects: 0–1 Test; Aedes - parasitology; Animals; Dengue - epidemiology; Dengue - transmission; Dengue fever; Deterministic chaos; Disease Outbreaks - statistics & numerical data; Humans; Insect Vectors - parasitology; Mathematical Concepts; Mathematical model; Models, Biological; Multiple subclasses; Nonlinear Dynamics; Seasonality; Seasons
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2013.11.003

•Irregular seasonal patterns are frequently observed in dengue outbreak data.•We introduce a multi-subclass dengue model with a seasonally varying vector population.•The complexity of the system as the degree of seasonality increases is investigated.•Higher seasonality results in more complexity in the solutions types.•Use of the 0–1 test confirms the existence of deterministic chaos for high seasonality. In recent decades, dengue fever and dengue haemorrhagic fever have become a substantial public health concern in many subtropical and tropical countries throughout the world. Many of these regions have strong seasonal patterns in rainfall and temperature which are directly linked to the transmission of dengue through the mosquito vector population. Our study focuses on the development and analysis of a strongly seasonally forced, multi-subclass dengue model. This model is a compartment-based system of first-order ordinary differential equations with seasonal forcing in the vector population and also includes host population demographics. Our analysis of this model focuses particularly on the existence of deterministic chaos in regions of the parameter space which potentially hinders application of the model to predict and understand future outbreaks. The numerically efficient 0–1 test for deterministic chaos suggested by Gottwald and Melbourne (2004) [18] is used to analyze the long-term behaviour of the model as an alternative to Lyapunov exponents. Various solutions types were found to exist within the studied parameter range. Most notable are the existence of isola n-cycle solutions before the onset of deterministic chaos. Analysis of the seasonal model with the 0–1 test revealed the existence of three disconnected regions in parameter space where deterministic chaos exists in the single subclass model. Knowledge of these regions and how they relate to the parameters of the model gives greater confidence in the predictive power of the seasonal model.