Title

A Mathematical Model for Dengue Fever in a Virgin Environment

Author(s)

Jason K. BowmanFollow

Major

Mathematics

Advisor

Dr. Orlando Merino

Advisor Department

Mathematics

Date

5-2012

Keywords

Dengue; epidemiology; biological modeling; disease modeling, Cape Verde; aedes aegypti

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Abstract

Dengue is a mosquito-borne viral infection found in tropical and subtropical regions around the world. The disease was named in 1779 and the first recorded epidemic of it occurred simultaneously on three continents within the following decade. Dengue is characterized by flu-like symptoms and, while its symptoms are generally reported as quite unpleasant, is rarely fatal. However, in some cases patients can contract a more serious form of the disease, known as Dengue Hemorrhagic Fever, which is far more dangerous. The World Health Organization estimates that today over 2.5 billion people are at risk for Dengue (over 40% of the world’s population). Between 50 and 100 million cases of traditional Dengue occur globally per year, with an estimated additional 500,000 cases of the hemorrhagic variation. Four decades ago, the disease was endemic in only nine countries. Currently it is endemic in more than 100 countries, and is spreading.

A variety of characteristics complicate any attempt to study or model the Dengue virus. Foremost among these is that the virus exists in four serotypes. Infection from one serotype grants life-long immunity, but makes the patient more susceptible to the other three forms. There is also an elevated risk of contracting Dengue Hemorrhagic Fever from a secondary infection. Furthermore, endemic Dengue tends to appear cyclically, with each outbreak separated by several years. Thus, populations where Dengue is endemic (such as many parts of Asia and Latin America) and several serotypes exist are exceedingly difficult to accurately represent with a single mathematical model.

In this paper, a system of differential equations is used as a virus dynamics model, based off a Dengue epidemics model proposed by Pinho et. al (2010). A 2009 Cape Verde epidemic, the first in that country’s history, is chosen as the outbreak for this study because of its unique characteristics: a virgin environment with no immunities or increased susceptibilities to the various Dengue serotypes, and the existence of a single serotype through-out the epidemic. Due to this novel incidence of Dengue in Cape Verde and to minimal reporting, the data set for the epidemic is sparse. However, this shortcoming is dealt with by using an extended logistic model-fitting technique. Certain key parameter values in the differential equations model can then be found based on this fitting. Other parameters are taken from previous studies in similar environments. With these, the basic reproductive rate (R₀) can be calculated, giving a numerical measure of this particular epidemic's infectiousness. The validity of this differential equation model is then tested by comparing generated values to the fitted data.

The Cape Verde epidemic presents a valuable opportunity to study the behavior of the Dengue virus without the added complexity of immunity, increased susceptibility, or multiple serotypes. Furthermore, this simplified population is natural, and not the result of human data selection or manipulation. This paper represents the first attempt in existing literature to carefully apply existing Dengue models and theory to such a virgin environment.