Dengue virus is a deadly disease found in tropical and subtropical climates around the globe spread by female Aedes Aegypti mosquitoes. Half the world’s population is at risk of contracting dengue fever, with an estimated 100-400 million infections annually . Dengue fever is now classified by the World Health Organization as the most critical mosquito-borne disease globally and is endemic in over 100 countries. Prevention of dengue is dependent on vector-control including the use of insecticides, community awareness campaigns and insecticide -treated bednets (ITNs). However, more novel approaches have also been introduced, two of which will be examined in this project: Sterile Insect Technology (SIT) and Wolbachia infection.
Key Equations
Using Mathematical Modeling to Analyze the Effectiveness of Sterile Insect Technology and Wolbachia Infection Intervention Techniques on Incidence of Dengue in Mexico
References
Abstract
Results
SIT involves releasing sterile male Aedes mosquitoes into the natural ecosystem. These males will mate with females, who will hatch sterile eggs that will not hatch. Thus, it will drive the population numbers of Aedes mosquitoes down. This ensures that other mosquito populations that do not carry disease and are crucial to ecosystem function are not also affected by the intervention method.
Vector Control Methods
Sterile Insect Technology
Wolbachia Infection
Wolbachia bacteria is a bacteria that lives inside the cells of an organism and is maternally transmitted. The bacteria does not negatively affect the organism, humans, or the environment. Crucially, however, Wolbachia blocks diseases like dengue from growing in the bodies of Aedes mosquitoes. Thus, mosquitos infected with Wolbachia cannot carry dengue. Aedes mosquitoes do not carry Wolbachia, so in order to utilize this method, male Aedes mosquitoes are infected with the bacteria in a lab. Then these Aedes mosquitoes are released in dengue fever-affected areas, where they mate with females, passing down the bacteria to their offspring.
No Intervention
SIT Intervention
Wolbachia Intervention
Methods
First, the values of certain known parameters like the human birth rate and death rate were determined. Then, the SIRS model was fit to the Mexican dengue case data from 2016 in order to estimate unknown parameters. Using these parameters, simulations of SIT and Wolbachia were run using separate models developed by Okuneye et. al4, Enahoro et. al3, and Gumel et. al5. Then infection versus time graphs were plotted for Wolbachia infection and no intervention. Additionally, the R0 value was calculated for the use of Wolbachia for comparison with the R0 value of dengue. The R0 value indicates how many people will be further infected when one person has the disease. Then, for SIT the number of sterile mosquitoes and non-sterile mosquitoes were plotted versus time. The graphs and R0 values were used to analyze SIT and Wolbachia’s effectiveness in reducing dengue.
Key Equations (cont.)
Figure 1: Delani et. al1
Figure 2: NEA2
Results (cont.)
Dengue Transmission Equations
SIT Equations Wolbachia Equations
Discussion
SIT Equations Wolbachia Equations
The SIT model estimated the effects of 10,000 sterile mosquitoes being released every 14 days for a period of 3 years. The Wolbachia model estimated the effects of 5,000 Wolbachia infected mosquitoes being released into the wild. Without any form of intervention, the model predicts that over 60 million people will be infected cumulatively over the course of the disease, as shown on the plot. With Wolbachia intervention this number is shown to be less than 1,000 showing a dramatic decrease in the incidence, meaning that Wolbachia is an effective technique in reducing dengue. Additionally, the R0 value of dengue when Wolbachia infected mosquitoes were released was estimated to be .34 by the model utilized. The R0 value for dengue has been estimated to be 4.74 by Liu et. al6. The significant decrease in the R0 value also indicates that Wolbachia is effective in reducing dengue incidence. For SIT plots were created that showed the number of sterile and nonsterile mosquitoes in Mexico over time. The plot of the non-sterile mosquitoes showed the number of mosquitoes approaching zero, meaning that SIT will completely eliminate the Aedes mosquito population. This will, in turn, almost eliminate dengue because Aedes mosquitoes are dengue’s main carriers.
Conclusion and Future Studies
Human Dengue Transmission Dynamics
Mosquito Dengue Transmission Dynamics
Dengue Infected Humans
Dengue Infected Mosquitos
Non-Sterile Female Mosquitoes Over Time
Sterile Male Mosquitoes Over Time
It was found that the usage of SIT and Wolbachia infection are both effective ways to reduce dengue incidence in Mexico. In the future, this model can be applied to a myriad of different diseases around the world like Zika and Malaria (with appropriate modifications). Additionally, the model can be modified to take into account other parameters that were not included here, including temperature and precipitation, both of which affect mosquito populations. In the future, projects that utilize these models should aim to gather more data, as several parameters here had to be estimated, affecting the accuracy of the models.
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