Modeling Vector Control

In Phoenix, a program is in place to eradicate one of the pests associated with high levels of damage to cotton crops - the pink bollworm, the larval form of a grey moth that thrives in cotton producing areas of the United States, Mexico, Egypt and India. This pest-control program actually breeds these moths, then sterilizes them via radiation exposure, and releases them by the millions from planes flying over cotton fields. The idea is for these infertile moths to breed with the existing wild populations, so that subsequent generations continually decrease in size until they are eradicated. Thus far, the program has been quite successful - in 2011, not a single wild bollworm was found by scientists in the field.

This type of approach has been applied numerous times in efforts to control insect pests, and is credited with the local eradication of the screw-worm fly, the Medfly, the melon fly and the Mexican fruit fly. The sterile insect technique successfully saved the agricultural industry billions of dollars and offered an alternative to chemical controls and their associated issues.This method is also currently being applied to disease vector insect species, including the tsetse fly (the vector for African trypanosomiasis, or "Sleeping Sickness"), Anopheles mosquitoes (vectors for malaria), and Aedes mosquitoes (vectors for dengue and several other mosquito-borne diseases).

The approach is not without complications, however. Depending on the target species, multiple releases of sterile insects must occur over extended geographical areas and time-periods to ensure continuous population decline over several generations, and to guard against vector migration and range expansion. Also, the radiation treatment has an affect the health of the sterile insects, so that they are less effective at competing for mates. This again leads to the need for additional treatments. The cost of repeated treatments - in addition to the expense involved in setting up the sterilization program itself - is often prohibitive for countries where diseases such as dengue and malaria are at their worst, and must be weighed against the expected benefit in terms of lives saved and medical and other control costs prevented.

From a modeling perspective, vector-borne diseases can be more complicated than direct-transmitted diseases. The indirect path of transmission from one host (be it plant, animal, or human) to another requires a separate set of mathematical equations addressing the disease dynamics within vectors and vector-host interactions. To assess vector control programs such as the sterile insect technique, explicit modeling of vector population dynamics is required. From a static approach, this can be as straightforward as applying a multiplicative factor less than one to new vector birth cohorts following each successful release of sterile vectors. For a more dynamic approach, male and female vector populations can be modeled separately, with the immigration of sterile individuals essentially "diluting" the reproduction rate, reflected by a spatial probability distribution for successful pairing of two fertile vector individuals. Multiple treatments can then be modeled over a simulated period to assess any changes in host disease incidence levels. These results can be compared with simulations of other vector control methods to help guide decisions as to the most effective means of disease reduction, or included in economic analyses to weigh costs and benefits of disease control programs before expensive techniques are implemented on the ground.

The field of disease control has some exciting and promising techniques to offer, and mathematical modeling of these techniques can go a long way toward determining the best implementation of these techniques, or choosing between them. If your organization is interested in examining the implementation of disease control methods, contact MathEcology to learn more about how mathematical modeling can help!

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