Understanding dengue fever dynamics: a study of seasonality in vector-borne disease models

Abstract

Dengue fever dynamics show seasonality, with the disease transmission being higher during the warmer seasons. In this paper, we analyse seasonally forced epidemic models with and without vector dynamics. We assume small seasonal effects and obtain approximations for the real response of each state variable and also for the corresponding amplitude and phase via decomposition of the sinusoidal forcing into imaginary exponential functions. The analysis begins with the simplest susceptible-infected-susceptible (SIS) model, followed by the simplest model with vector dynamics, susceptible-infected-susceptible for hosts and uninfected-vector (SISUV). Finally, we compare the more complex susceptible-infected-recovered (SIR) and susceptible-infected-recovered for hosts and uninfected-vector (SIRUV) models and conclude that the models give basically the same information when we replace, in the SIR model, the human infectivity by a function of both human and mosquito infectivities.

Keywords:

• epidemic models
• disease vector dynamics
• seasonally forced models

2010 AMS Subject Classifications:

• 92B05
• 92D25
• 97M60

Acknowledgments

We would like to thank to the two anonymous referees for their comments and suggestions that improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Filipe Rocha http://orcid.org/0000-0001-6510-8440

Luís Mateus http://orcid.org/0000-0002-4728-3963

Urszula Skwara http://orcid.org/0000-0002-9549-3199

Maíra Aguiar  http://orcid.org/0000-0001-8354-9944

Nico Stollenwerk  http://orcid.org/0000-0001-9315-5586

Additional information

Funding

This work has been supported by the European Union under FP7 in the DENFREE project [grant number 282378] and Fundação para Ciência e Tecnologia (FCT), Portugal, via the projects PTDC/MAT/115168/2009 and UID/MAT/04561/2013.