Spread of Zika in Brazil Using the Ross-MacDonald Model

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The spread of the Zika virus throughout a population can be modeled using equations that depend on the time elapsed after the initial outbreak and the average temperature in the region.


In this Demonstration, you can select states of Brazil with preset temperatures for each. You will see the rate of spread as a red dot on the graph and a map of the state that turns more red in proportion to the spread of the virus.

The Demonstration illustrates the rate at which populations can be infected by Zika, in the absence of preventive measures such as treatment or quarantine.


Contributed by: Jessica Lu and John Kwak (June 2016)
Special thanks to the University of Illinois NetMath Program and the mathematics department at William Fremd High School.
With additional contributions by: Christopher Grattoni
Open content licensed under CC BY-NC-SA




[1] E. B. Hayes, "Zika Virus Outside Africa," Emerging Infectious Diseases, 15(9), 2009. wwwnc.cdc.gov/eid/article/15/9/09-0442_article.

[2] L. B. Carrington, M. V. Armijos, L. Lambrechts, C. M. Barker, and T. W. Scott, "Effects of Fluctuating Daily Temperatures at Critical Thermal Extremes on Aedes aegypti Life-History Traits," PLOS One, Mar 8, 2013. journals.plos.org/plosone/article?id=10.1371/journal.pone.0058824.

[3] L. Lambrechts, K. P. Paaijmans, T. Fansiri, L. B. Carrington, L. D. Kramer, M. B. Thomas, and T. W. Scott, "Impact of Daily Temperature Fluctuations on Dengue Virus Transmission by Aedes aegypti," Proceedings of the National Academy of Sciences of the United States of America, 108(18), 2011 pp. 7460–7465. www.ncbi.nlm.nih.gov/pmc/articles/PMC3088608.

[4] R. Maciel-de-Freitas, Á. Eiras, and R. Lourenço-de-Oliveira, "Calculating the Survival Rate and Estimated Population Density of Gravid Aedes aegypti (Diptera, Culicidae) in Rio de Janeiro, Brazil," Saúde Pública, 24(12), 2008 pp. 2747–2754. www.scielo.br/scielo.php?script=sci_arttext&pid=S0102-311X2008001200003.

[5] Wikipedia. "States of Brazil." (Jun 13 2016) en.wikipedia.org/wiki/States_of_Brazil.

[6] WeatherSpark. "Beautiful Weather Graphs and Maps." (Jun 13, 2016) weatherspark.com.

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