We illustrate different modeling approaches to describe the dynamics of dengue fever (a vector-borne disease). According to the Center for Disease Control and Prevention (CDC), there are an estimated 50 to 100 million cases of dengue fever (the symptoms associated with dengue infection) every year around the world (mostly in the tropics) 1. We demonstrate that “effective” mosquito control strategies are not sufficient in controlling dengue outbreaks. It is possible for low mosquito densities to cause large outbreaks. Furthermore, mosquito eradication is likely the most effective way to eliminate dengue fever but it is unpractical and nearly impossible to achieve. Based on the epidemiological threshold, R0, we were able to determine the most sensitive parameters that can lead to enhance the implementation of public health policies and control strategies under different modeling scenarios.

Alcohol abuse has been a problem for a long time in the United States. Drinking behavior patterns have changed over the years and it affects all races, age classes and social status. We used epidemiological approaches and constructed mathematical models to study drinking behavior. We find that peer pressure from moderate drinkers have the biggest impact on the population of low-risk drinkers. Threshold quantities that establish the prevalence of the drinking communities are studied and thoroughly analyzed to determine possible prevention strategies. We also explored the effect of the SDR (susceptible (’at-risk’), drinkers, temporarily recovered) model on a ’small-world’ structure and a continuous time Markov chain model. We found that network structure does not play a role on drinking behavior dynamics. We conclude that the SDR model is robust. For the stochastic simulations we computed final size drinker distributions. We also explored a more detailed model that includes four drinker classes (abstainers-occasional drinkers-moderate drinkers-heavy drinkers) and n neighborhoods. We computed threshold conditions and conducted an uncertainty analysis. We determine that the key transition to have an endemic drinking culture is from occasional drinker to moderate drinker.

1CDC: Fact Sheet: Dengue and Dengue Hemorrhagic Fever. June 19, 2001. World Wide Web. http://www.cdc.gov/ncidod/dvbid/dengue/facts.htm