Ew—looks like the workplace flu has finally gotten to you. Rather than spread your germs to the rest of your coworkers, you call in a sub and stay home with a can of soup and some soothing Netflix. But by calling in a substitute worker—common wisdom and even a requirement in many workplaces—you could be inadvertently spreading the disease more widely.

That’s the suggestion of a new study published in the journal Nature Physics. Using data modeling, a group of mathematicians and physicists found that when sick people with “essential societal roles”—think first responders and teachers who often call in outside help when ill—are replace with healthy substitutes, disease can spread more quickly and affect more people than if no substitute were called in.

It may seem counterintuitive, but it’s supported by the numbers. Imagine a social group of nine people and one sick one. The sick one goes home and in comes a random person as a replacement. Everyone in the group can be considered “sick,” or susceptible to being ill. But that type of model doesn’t take something into consideration, say the study’s authors. In real life, the sub is not chosen at random—they are chosen because they are healthier than the person who has fallen ill.

That introduces a new risk factor into the equation. Though the sick person may not be at the peak of contagion—and their social group is already at higher risk for illness—the healthy person enters a “sick” environment. Not only could they become infected themselves, but they could then spread the infection to their own healthy social group.

This theory held up in the team’s analysis: When actual outbreak data was used, it showed an association between healthy replacements and the spread of diseases like influenza.

“If it were just one or two people being replaced, really nothing would happen,” Samuel Scarpino, the study’s lead author, tells Smithsonian.com. But in a large population—say, a school district that regularly brings in substitutes—the effect can be exponential. So even if you stay home to stem the sickness, your substitute could, ironically, spread it even further.

Though the study did not look at the effects of people simply staying home without a replacement, it may factor in to the ongoing conversation about sick leave in the United States. There is no federal requirement for employers to provide sick leave, but some states have sick leave laws. In states like New Jersey, it is illegal for employers to require their workers to find replacements in order to obtain leave.

But it may not be necessary to quit using replacement workers altogether, says Scarpino. “If the substitutes or replacements were vaccinated before coming into [a sick worker’s] role, that would replace the accelerating spread.” And there’s another potential solution for businesses like schools and hospitals that regularly use substitute workers, Scarpino notes. “If we replace people very quickly, then there is little to no effect on the replacement.”

Another factor that could slow the spread is rapid reporting of illness. By workers waiting to report sickness—or not staying home once they become ill—their replacements are more likely to spread disease rapidly. But changing that will go against national norms: A recent poll conducted by NPR and the Harvard T.H. Chan School of Public Health found that nearly two-thirds of working adults still go to work always or some of the time when they have the flu.

Given that sick leave and sufficient paid time off is unavailable to so many—and some bosses reward workers for staying on the job no matter what—changing the rate at which substitute workers spread disease may be as difficult as kicking a nasty bug.