Health misinformation can exacerbate infectious disease outbreaks. Especially pernicious advice could be classified as "fake news": manufactured with no respect for accuracy and often integrated with emotive or conspiracy-framed narratives. We built an agent-based model that simulated separate but linked circulating contagious disease and sharing of health advice (classified as useful or harmful). Such advice has potential to influence human risk-taking behavior and therefore the risk of acquiring infection, especially as people are more likely in observed social networks to share bad advice. We test strategies proposed in the recent literature for countering misinformation. Reducing harmful advice from 50% to 40% of circulating information, or making at least 20% of the population unable to share or believe harmful advice, mitigated the influence of bad advice in the disease outbreak outcomes. How feasible it is to try to make people "immune" to misinformation or control spread of harmful advice should be explored.