According to the American Mosquito Control Association, mosquitoes cause more human suffering than any other organism. Over one million people worldwide die from mosquito-borne illnesses each year. These diseases—transmitted by biting—include dengue fever, chikungunya, and Zika virus, among others. Dengue and chikungunya can be life-threatening; symptoms include high fever and muscle and joint pain. While those who contract Zika often exhibit mild to nonexistent symptoms, the virus is especially dangerous for pregnant women; babies of mothers with Zika are prone to severe birth defects, including microcephaly and abnormal brain development.
Because no vaccine exists for the aforementioned infections, mitigation strategies typically focus on other methods of control. Such methods include the elimination of breeding habitats, like still water in water tanks or scrap ties; the introduction of natural predators, such as fish that consume larvae populations; and perhaps most notably, the spraying of insecticide. Although spraying is the most common approach, it is financially expensive, logistically challenging in both highly-urban and highly-remote areas, and typically not sustained long enough to eradicate infected populations. Thus, despite these efforts, mosquitoes—and mosquito-borne infections—continue to plague human populations. In response, public health researchers have recently suggested introducing Wolbachia bacteria to mosquito populations to control their spread of disease — the creation of one epidemic to stop another.
In a contributed presentation at the 2017 SIAM Annual Meeting, currently taking place in Pittsburgh, Pa., Zhuolin Qu of Tulane University presented an ordinary differential equation (ODE) model to measure the mitigation success of infecting mosquitoes with Wolbachia. “Instead of killing the mosquitoes, we let them live but infect them with Wolbachia so they can’t transmit the diseases to humans,” Qu said. Wolbachia is a natural parasitic microbe frequently found in various arthropods; it is present in about 60 percent of insects, and halts the reproduction of harmful viral strains inside mosquitoes. Infected female mosquitoes transmit Wolbachia to their offspring. When both male and female mosquitoes are healthy, their offspring are also healthy. But when a female is infected with Wolbachia, its offspring automatically is too, regardless of the male’s health status. And if only the male is infected, cytoplasmic incompatibility prevents the pair from reproducing.
These reproductive dynamics led Qu to wonder how many Wolbachia-infected mosquitoes must be released into the wild for the strategy to be effective. “It’s difficult to sustain a stable infection because small infections are wiped out, and the infection is not usually found naturally in Aedes aegypti mosquitoes,” Qu said. Aedes aegypti is the primary transmitter of dengue, chikungunya, and Zika. Additionally, an accompanying fitness cost affects the mosquitoes’ ability to survive and replicate, as Wolbachia shortens the female lifespan and limits the number of eggs produced.
Qu proposed an ODE model to capture the complex vertical transmission cycle of Aedes aegypti and analyze the tipping point/threshold condition necessary to maintain a stable Wolbachia endemic. Her model accounts for heterosexual transmission, the carrying capacity for the aquatic larval stage, and the multi-stage female life cycle. Qu separated pregnant females from the rest of the population to avoid further contact with males, because females are able to lay eggs repeatedly after obtaining sperm.
Threshold condition for Wolbachia transmission. Image credit: Zhuolin Qu, AN17 presentation.
Qu then introduced the basic reproductive number, \(R_0\). “In epidemiology, the \(R_0\) of an infection is the total number of cases one case generates within its infectious period in a totally susceptible population,” she said. Qu used a next-generation matrix approach to calculate \(R_0\), the ratio of new infected eggs generated by an infected egg
over new uninfected eggs generated by an uninfected egg in one life-cycle of the mosquito. She conducted bifurcation analysis to determine the steady state and identify the critical threshold condition for Wolbachia transmission. When \(R_0<1\), the number of infected mosquitoes decreases and the infection dies out. But when \(R_0>1\), the infection spreads throughout a population.
Qu also explored possible ways to integrate a Wolbachia outbreak with pre-release mitigation strategies to maximize control. “If we remove some of the natural population before the release, we can alter the threshold level and speed up infection,” Unsurprisingly, she found that Wolbachia was most effective when combined with residual spraying, rather than use of sticky traps, larval control at the aquatic stage, and acoustic attraction.
Though researchers in the United States have not actually released Wolbachia bacteria into the wild, Australia has seen several real field releases and instances of the targeted mosquito-borne illnesses have decreased. Ultimately, Qu hopes that her model will inspire a more permanent suppression of mosquito-borne illnesses not yet treatable with vaccinations.
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|| Lina Sorg is the associate editor of SIAM News.