Given a mosquito's vastly shorter life span, preventing the spread of the infection to more human hosts greatly reduces the number of viable parasites in existence (CDC 2009). 10)

There are several reasons that viral infections are more difficult to treat and diagnose than bacterial infections. For one thing, viruses are not truly alive, and this makes it difficult to kill them. They are essentially packets of genetic information in tough protein shells; there are no real biological mechanisms for medicines to disrupt. In addition, the virus' use of host cells as reproduction sites means that drugs used to attack the virus often als due damage to healthy...

The basic life cycle of an animla virus includes hijacking a host cell and reproducing until rupture, where the process continues in new host cells. Most viruses can remain viable indefinitely outside a host, so the death of the host is immaterial. All of these factors lead to viral infections being far more dangerous than many bacterial infections; once the virus has entered a host, there is often little to be done but treat the symptoms and assist the body's natural defenses against the invading agent.
Reference

CDC. (2009). "Malaria." Accessed 22 September 2009. http://www.cdc.gov/Malaria/index.htm