Disclosed is a method for slowing down the spread of viruses by limiting the number of Transmission Control Protocol ("TCP") connection attempts to arbitrary Internet Protocol ("IP") addresses that can be in progress at any given time--a common method employed by viruses to spread to other hosts from an infected host. This is achieved by setting a small limit on the number of connection attempt requests that can be in progress at any given time and can be implemented regardless of whether anti-virus software is installed on the system.