A simple periodic-forced model for dengue fitted to incidence data in Singapore

doi:10.1016/j.mbs.2013.04.001

Mathematical Biosciences

Volume 244, Issue 1, July 2013, Pages 22-28

https://doi.org/10.1016/j.mbs.2013.04.001 Get rights and content

Highlights

•
Fit of a periodic model to dengue incidence data in Singapore from 2003 to 2007.
•
Estimation of the parameters governing the vector population dynamics.
•
Estimation of the impact of vector-control.
•
Close relationship between vector density and temperature.
•
Hypothesis explaining partially the 2007 dengue outbreak in Singapore.

Abstract

Dengue is the world’s major arbovirosis and therefore an important public health concern in endemic areas. The availability of weekly reports of dengue cases in Singapore offers the opportunity to analyze the transmission dynamics and the impact of vector control strategies. Based on a previous model studying the impact of vector control strategies in Singapore during the 2005 outbreak, a simple vector-host model accounting for seasonal fluctuation in vector density was developed to estimate the parameters governing the vector population dynamics using dengue fever incidence data from August 2003 to December 2007. The impact of vector control, which consisted principally of a systematic removal of actual and potential breeding sites during a six-week period in 2005, was also investigated. Although our approach does not account for the complex life cycle of the vector, the good fit between data and model outputs showed that the impact of seasonality on the transmission dynamics is highly important. Moreover, the periodic fluctuations of the vector population were found in phase with temperature variations, suggesting a strong climate effect on the vector density and, in turn, on the transmission dynamics.

Introduction

Dengue is the major arbovirosis in the world with more than 50 million dengue fever cases per year [1], [2]. Although most dengue cases remain asymptomatic or present mild symptoms, Dengue Hemorrhagic Fever (DHF) and Dengue Shock Syndrome (DSS) are the most severe expressions with case-fatality rates (CFR) generally close to 1% [3], [4]. Four immunologically distant serotypes were identified and coexist in many hyperendemic areas [5], [6]. The first dengue cases in Singapore were described in the 1960s and dengue became rapidly a major cause of childhood death. The Singapore government initiated a vector control programme in 1968 resulting in a reduction of the premises index, i.e. the percentage of inspected premises found to have containers with Aedes aegypti larvae or pupae, from 16% to 2% in 1973. Since then, the premises index has remained around 2% and Singapore is now recognized as having one of the most effective vector control policies in the world [7], [8]. Despite relatively low dengue activity over more than 15 years, Singapore experienced several dengue outbreaks since the 1990s which might be due to different factors [8]. The largest outbreak occurred in 2005, with more than 14,000 identified symptomatic cases. During this epidemic, emergency vector-control measures, mainly based on removal of breeding sites, were set up, allowing for a rapid decrease of dengue case notifications. However, another large outbreak occurred in 2007, after one year with low dengue activity.

A wide range of mathematical models was developed to study the transmission process of the dengue virus [9]. Most of these models were derived from the simple vector host model originally proposed by Bailey [10], with different adaptations (e.g. age-structure [11], [12], detailed vector lifecycle [13], [14], [15], [16]; multi-serotypes [17], [18], [19], [20]; etc). However, following the multi-strain model of Ferguson et al. [21], several models considered direct transmission between hosts, assuming the time scale for transmission to be sufficiently short and the mosquito population sufficiently dense to ignore the vector component [22], [23], [24], [25]. Although dengue outbreaks often exhibit 3- to 5-year inter-epidemic periods, which could be reproduced with multi-serotype host-to-host transmission models, intra-annual fluctuations of dengue incidence were shown to be linked with seasonality, acting on the vector population [14], [17], [20], [26]. Moreover, Yang and Ferreira [16] showed that seasonality can also influence the effectiveness of vector strategies by identifying the optimal period to initiate larvicide or adulticide application.

Burattini et al. [14] proposed a transmission model assuming seasonal variations in the development rate from eggs to adult stages. Moreover, in addition to a periodic forcing governing the seasonal fluctuation of the vector population, the “egg carrying capacity” was assumed to increase linearly with time in relation with the observed increase in temperature. Using this framework, Burattini et al. tested the impact of different control strategies and reproduced qualitatively the dengue incidence data in Singapore from 2003 to 2006. This model was further used by Massad et al. who assumed that the presence of haze in Singapore could impact on mosquito behavior, explaining the reduction in dengue activity in 2006 [27]. Although this model provided a good qualitative fit to data, the comparison of dengue incidence time series with the pollution index showed no evidence of any relationship between dengue activity and haze [28], [29].

The aim of the present study was to evaluate the vector population dynamics from dengue fever incidence data. As suggested by Burattini et al. [14], the incidence data in Singapore offer the opportunity to quantify the impact of emergency control measures. For that purpose, we focused our analysis on a restricted time-window running from August 2003 to December 2007. To avoid overparametrization we developed a simplified version of Burattini’s model, accounting exclusively for the adult vector population with a periodic recruitment rate. Although the emergency vector control strategy carried out in September 2005 focused principally on breeding site removal, we evaluated the impact on the adult mosquito population. Finally, the analysis of data post-intervention permitted to formulate a hypothesis to explain the dynamics of infection observed after the period of control.

Section snippets

Model formulation

Based on the model of Burattini et al. [14], the host population, denoted by the index h, is divided into three compartments according to their status : susceptible ( $S_{h}$ ), infectious ( $I_{h}$ ) and ( $R_{h}$ ) recovered individuals. The intrinsic incubation period (IIP) was not represented in the model because of its relatively low impact on the transmission dynamics, as shown by Newton and Reiter [30]. Conversely, the extrinsic incubation period (EIP) lasts between 10 and 12 days for an average mosquito

Results

In the period prior to emergency vector control, the peak in dengue incidence was found to occur in October each year from 2003 to 2005, showing a lag of 16.8 weeks with the maximal vector density (Fig. 1). Studies on the impact of climate variability on dengue incidence in Singapore also reported a correlation between temperature and dengue incidence with a possible time lag up to 20 weeks [35], [47]. Recently, Hii et al. analyzed dengue incidence in Singapore using weather data highlighting an

Conclusion

The aim of the present study was to estimate the parameters governing the adult vector population dynamics from dengue fever case notifications in Singapore. For that purpose, a simple vector-host transmission model was adapted from a previous model, which reproduced Singaporean data between 2003 and 2006 qualitatively well. Burattini et al. developed a vector-host transmission model including eggs and adult stages for the mosquito population [14]. Seasonality was incorporated into the model

Acknowledgements

The authors want to thank the two referees and the associate editor for their comments, which greatly improved the manuscript. NH also acknowledges support from the UA Scientific Chair in evidence based vaccinology.

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¹: Address: Centre for Health Economics Research and Modelling Infectious Diseases (CHERMID), Vaccine & Infectious Disease Institute, University of Antwerp, Campus Drie Eiken, Universiteitsplein 1, 2610 Antwerpen, Belgium.

²: Address: Interuniversity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Agoralaan 1, Building D, 3590 Diepenbeek, Belgium

³: Address: Faculty of Medicine, The University of New South Wales, Sydney, NSW 2052, Australia

View full text

A simple periodic-forced model for dengue fitted to incidence data in Singapore

Highlights

Abstract

Introduction

Section snippets

Model formulation

Results

Conclusion

Acknowledgements

The Lancet

J. Pediat.

Lancet

Trends Microbiol.

The Lancet

Math. Comput. Model.

Math. Biosci.

Epidemics

Ecol. Model.

Appl. Math. Comput.

Appl. Math. Comput.

J. Theor. Biol.

Trends Parasitol.

The Lancet

J. Theor. Biol.

Dengue and dengue hemorrhagic fever

Clin. Microbiol. Rev.

Global spread and persistence of dengue

Annu. Rev. Microbiol.

Dengue prevention and 35 years of vector control in Singapore

Emerg. Infect. Dis.

Dynamic epidemiological models for dengue transmission: a systematic review of structural approaches

PLoS ONE

The Mathematical Theory of Infectious Diseases and its Applications

Modelling the control strategies against dengue in Singapore

Epidemiol. Infect.

The seasonal pattern of dengue in endemic areas: mathematical models of mechanisms

Trans. R. Soc. Trop. Med. Hyg.

Ecological and immunological determinants of dengue epidemics

Proc. Natl. Acad. Sci. USA.

The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens

Proc. Natl. Acad. Sci. USA

Asymmetry in the presence of migration stabilizes multistrain disease outbreaks

Bull. Math. Biol.