Mathematical model predicts dengue epidemic in urban areas

A new mathematical model developed by three American scientists offers a simplified approach to studying the spread of dengue fever in urban areas by breaking down the epidemic dynamics across a city and its varying neighbourhoods and populations.

Authored by Lucas M. Stolerman, Daniel Coombs and Stefanella Boatto, the 'SIR-Network Model and its Application to Dengue Fever,' offers a useful insight into how varying neighborhood conditions affect the spread of the disease and ways to contain it.

"The SIR-Network model can be used to predict whether local interventions - like cleaning up standing water in containers - in one or two neighbourhoods could affect the prevalence of Dengue across the city," said study co-author Coombs.

"We give formulae that describe whether an epidemic is possible, in terms of human travel patterns among neighbourhoods, mosquito populations and biting rates in each neighbourhood," he added.

The model uses a Susceptible-Infected-Recovered (SIR) approach to disease spread and the network consists of the city's neighbourhoods where local populations are assumed to be well-mixed.

The authors applied the SIR-Network model to Dengue fever data, which had been updated several times, including as recent as 2014, from the epidemic outbreak of 2007-2008 in various neighbourhoods of Rio de Janeiro, Brazil, and soon discovered several interesting features of the epidemic.

First, they needed to include a transmission rate that varied over the months of the Dengue season to match the available data. The authors predict that the transmission rate peaks 6-8 weeks before the peak incidence of Dengue.

Secondly, they predict that the city centre, where large populations from various neighbourhoods go to work each day, is the most important neighbourhood to spreading the fever. Ultimately, the researchers found that results were improved most when a time-infection parameter was introduced to model seasonal climate changes.

"We feel that our results highlight the need for countermeasures before the peak of an epidemic, and also point to the importance of central neighbourhoods as hubs of Dengue transmission," said Boatto.

The study co-authors admit establishing a comprehensive picture of Dengue would be very challenging because there are so many varying pieces to the puzzle. For example, some of the factors to be considered include the impact of environmental variables on mosquito populations, changes in weather, human behaviour like mosquito avoidance or control and travel on the network.

The model was published recently in the Society for Industrial and Applied Mathematics (SIAM) Journal on Applied Mathematics.