The best way to treat influenza infection is to prevent it from occurring in the first place. Each year, a flu vaccine produced against the most likely subtypes of influenza A and B is available, and is recommended for people with high-risk medical conditions such as asthma. This vaccine has been shown to prevent or reduce the severity of infection as well as the complications from infection. Vaccination should be given annually in order to provide protection against that years influenza subtypes as well as to provide a boosting effect, as protection from the vaccine begins to fade after one year. While it is not yet known if the influenza vaccine protects against infection by the swine flu, I suspect that the severity of the infection would be lessened, if not prevented, with the influenza vaccine.
In addition, good hygiene can be helpful in preventing influenza. Frequent hand washing, or the use of alcohol-based hand cleaners (such as Purell), can help prevent the transmission of the influenza virus. People with influenza infection should minimize going to public places, should cover their mouths when sneezing or coughing, and should avoid sharing food and drink with other people.
However, since many people dont get influenza vaccinations, and because these vaccinations arent perfect, asthmatics do become infected with the flu. Many medications are available for the treatment of influenza infections which have been shown to reduce the severity and duration of symptoms when taken within 48 hours of the start of the illness. These medications can also be used to reduce the chance of infection when someone is exposed to a person with influenza.
Amantadine/Rimantadine
These anti-viral medications have been available for decades, and are useful in the treatment and prevention of influenza A infection, but not for influenza B. Amantadine and rimantidine probably work by preventing the influenza virus from infecting and replicating inside the cells of a persons respiratory tract. Side effects of these medications can be severe and often limit their use; rimantadine tends to have less severe side effects than amantadine.
Zanamavir/Oseltamivir
These newer anti-viral medications are effective for the treatment and prevention of infection from influenza A and B. Zanamavir is an inhaled medication, while oseltamivir is an oral medication; both work by preventing the influenza virus from replicating inside the cells of a persons respiratory tract.
During the 2008 to 2009 influenza season, the Food and Drug Administration reported that a particular subtype of influenza A was nearly completely resistant to oseltamivir. The recommended treatment for influenza A of unknown subtype (or the resistant subtype) is therefore zanamavir or the combination of oseltamivir and rimantadine. The preferred treatment for non-resistant subtypes of influenza A or influenza B is zanamavir or oseltamivir.
Swine flu, which is a mutated type of influenza A, has been shown to be resistant to treatment with amanatadine and rimantadine, but zanamivir and oseltamivir are effective treatments for swine flu.
Learn more about the treatment of influenza in asthmatics.
Sources:
Nathan RA et al. Management of Influenza in Patients With Asthma or Chronic Obstructive Pulmonary Disease. Ann Allergy Asthma Immunol. 2001;87:447-54.
Interim Guidance on Antiviral Recommendations for Patients with Confirmed or Suspected Swine Influenza A (H1N1) Virus Infection and Close Contacts. Centers for Disease Control Website. Accessed April 28, 2009.
Fiore AE, et al. Prevention and Control of Influenza: Recommendations of the Advisory Committee on Immunization Practices (ACIP), 2008. MMWR. August 8, 2008 / 57(RR07);1-60.
DISCLAIMER: The information contained in this site is for educational purposes only, and should not be used as a substitute for personal care by a licensed physician. Please see your physician for diagnosis and treatment of any concerning symptoms or medical condition.

