The EPA has a useful guide on pests and diseases they carry. Pests like mosquitoes and ticks can carry infectious pathogens such as Zika virus and Lyme disease. Rodents and unwelcome wildlife could have rabies, and many people are allergic to cockroaches, which can trigger asthma or other allergic reactions. Some pests are dangerous not because of a disease they carry, but because of a toxin they produce. Read more about poisonous pests in Dallas.