How to get a tenant to move out after lease expiration

[Christy Wright]

Is a court ordered eviction the only way to force a tenant out of a property after their lease has expired? We gave this tenant a 45-day notice in writing that we would not be renewing their lease. We cannot prove it, however we are quite certain there is plenty of drug activity going on in this apartment, not to mention they are constantly disturbing other tenants with screaming. this property is located in Missouri. Any other ideas, besides court order eviction?