In many parts of the U.S., the frigid month of January isn't the time most people think about mosquitoes. However, with the government shutdown already the longest in U.S. history (as of this writing), thinking about warmer months (including the biting insects they bring) might be a welcome relief.
Mac Hyman is an applied mathematician at Tulane University in New Orleans and a past president of the Society for Industrial and Applied Mathematics (SIAM). His tries to "find ways that math can help make the world a better place," he said.
Hyman began mathematically modeling the spread of infectious diseases in the 1980's. Back then, he studied the spread of HIV. His recent research focuses on using the power of mathematical modeling to inform mosquito control aimed at preventing the spread of Zika, dengue, chikungunya and other mosquito-borne infectious diseases.
Here's the scoop:
The mosquito Aedes aegypti, commonly called the yellow fever mosquito, "is the primary species responsible for transmitting viruses such as Zika, dengue and chikungunya between people. In some communities, other mosquitoes may also contribute to transmission, but their contribution is minor," according to the World Mosquito Program, a not-for-profit initiative that focuses on protecting people from mosquito-borne diseases.
There's a type of maternally-transmitted bacteria called Wolbachia pipientis that's naturally present in about 60% of insect species, including some species of mosquitoes. That bacteria inhibits the transmission of certain pathogens to humans. However, Wolbachia isn't naturally found in A. aegypti.
With the life-threatening nature and lack of effective vaccines for many diseases transmitted by A. aegypti, it's critical that researchers search for viable ways to thwart the threats these mosquitoes pose to people. However, "While most mitigation strategies aim to eliminate popular mosquito breeding sites through the use of insecticides, the accompanying costs, logistical difficulties, and resistance evolution make these treatment methods unsustainable," according to a SIAM News Blog piece by Lina Sorg.
One control strategy that appears promising? Introducing Wolbachia into wild A. aegypti mosquito populations by releasing ones previously infected in a lab. This may sound simple, but it's challenging to produce a situation in which the bacteria remain present in wild mosquito populations without the need for re-introduction.
"Mosquitoes don't stay put. They fly away, there's wind, there's diffusion," said Hyman. "The key to understanding what's going on is these mathematical models."
Using ordinary differential equations, Hyman and his collaborators evaluated which method is most effective for introducing a self-sustaining Wolbachia infection in wild A. aegypti populations. "Differential equations are the tools to model systems that change in time," he said. Past studies also focused on using ordinary differential equations for this purpose, but they have had limitations that aren't present in the models presented in the recent one, which was published in the SIAM Journal on Applied Mathematics. For instance, some previous models didn't account for all mosquito life stages.
The team's "two-sex model accounts for the aquatic life stage, heterosexual transmission, and multiple pregnant states for female mosquitoes, thus capturing the entire transmission cycle," the SIAM News Blog post notes.
Depending on the environmental conditions, about 30% to 40% of mosquitoes must be infected in an area in order for that infection to be self-sustaining, Hyman said.
Hoping pesky mosquitoes will be eliminated through this effort? Look elsewhere. The focus of this research is managing mosquito populations so fewer humans become sick or die as the result of mosquito-borne illnesses, not eliminating mosquitoes altogether, Hyman said.
In that vein, researchers analyzed which of several strategies (including indoor residual spraying, larval control related to water storage and containers where mosquitoes commonly breed, sticky gravid traps for attracting and killing uninfected pregnant females and acoustic attraction, a method for reducing the number of uninfected males) were most effective for use before the release of Wolbachia-infected mosquitoes.
"Our simulations indicate that the pre-release mitigations that target pregnant females, such as residual spraying and sticky gravid traps, are more helpful than ones that target only males or the aquatic stage, given that pre-release mitigation stops once the release starts,” study author Zhuolin Qu, who is also an applied mathematician at Tulane University, stated in the SIAM News Blog post.
For the next stage of the project, the team will focus on incorporating spatial effects into their models, a stage of the project that will rely heavily on a different mathematical tool: partial differential equations. They also plan to use data from field trials conducted through the World Mosquito Program to validate their current models, Hyman said.
"Math is the language that we can use to really understand these complex phenomenon...Don't underestimate the importance that math can have in making the world a better place," he said.
