# Mathematical model could help predict dengue fever epidemic

Scientists have developed a new mathematical model that could predict the spread of dengue fever in urban areas and may help contain the deadly disease.

Washington: Scientists have developed a new mathematical model that could predict the spread of dengue fever in urban areas and may help contain the deadly disease.

The model created by Lucas M Stolerman and Stefanella Boatto from Universidade Federal do Rio de Janeiro offers a simplified approach to studying the spread of the dengue fever in urban areas, specifically breaking down the epidemic dynamics across a city and its varying neighbourhoods and populations.

The model is important for studying how varying neighbourhood conditions affect the spread of dengue fever and how to contain it. For example, some neighbourhoods have standing water allowing large mosquito populations to develop. Since mosquitoes fly only a few hundred metres from their birthplace, a human infected with the disease who commutes long distances could spread the disease.

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 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 coauthor Daniel Coombs, professor at the University of British Colombia in Canada.

"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," Coombs said. The fraction of people travelling from residential neighbourhoods to active ones are represented by directed edges in the network.

The study also presents fundamental properties of the basic reproduction number (Ro) for their specific model. Ro is the expected number of secondary cases due to a single infection.

The researchers 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 researchers predict that the transmission rate peaks 6 to 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.

The study was published in the SIAM Journal on Applied Mathematics.

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