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.
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