The law regarding landlords and tenants is Iowa Code Ch. 562A. Part 2 (§562A.27 et seq.) states the legal remedies available to a landlord. §562A.27 specifically spells out the remedies for material non-compliance with lease terms. The gist of that and related sections is that if a person is in violation of a lease, there is a legal process that has to be followed, and if successful, the sheriff will forcibly evict the tenant (though §562A.27A, the clear and present danger section, shortens the process – still, it's not immediate and it does require legal notice etc.).
Under the law, you (apparently) have become a landlord and have an unwritten tenancy agreement with the tenant. I assume based on your description of the facts you have a long-term written agreement with the property owner. By allowing this person to live with you, you have entered into a landlord-tenant relationship, which limits your rights. The police will not respond to this situation – a legal squabble – whereas if someone broke into your residence and was trespassing (and you complain in a timely manner, not allowing the person to trespass), the police would respond and not require a court order.
§562A.9(5) states that in lieu of a specific term of tenancy, in the case of a roomer paying weekly rent the tenanct period is a week, otherwise it is a month. §562A.6 defines "roomer": basically, if you are a "roomer", so is your sub-lessor.
By agreeing to let the person stay with you, you have become a landlord and sub-lessor, thereby subject to the restrictions on landlord actions. That means you have to take the person to court to get rid of them. Failure to pay agreed-on rent is certainly sufficient legal cause, and any monthly lease can be terminated by the landlord after giving legal notice (30 days advance notice).