Soma is a kind of opiate in Brave New World that causes people to feel happy so that they don't concentrate on the reality that they live in a dictatorship. Soma is described as having “all the advantages of Christianity and alcohol; none of their defects.” It allows its users to take a short break from reality and return without a headache and without the need to harbor the mythology of religion. People (such as Bernard and Lenina) take soma with their coffee before they go out to socialize at night, and there are ice-cream soma bars. The people are so used to taking soma, that they find it impossible and frightening to face life without it. Soma is used to maintain social order and keep people from feeling any negative human emotions, such as jealousy, depression, sadness, or anxiety.

Soma cannot be compared to Prozac, as Prozac is intended to help people who suffer from depression have the equanimity to handle their lives and their real clinical condition. Prozac does not cause euphoria, and it does not remove people from reality. Instead, it helps people who suffer from an illness treat that illness, just as people who suffer from myopia need to wear glasses. Myths about depression and Prozac abound, but there is scientific fact that depression is a true disorder and that Prozac and other anti-depressants help people function and enable them to deal with reality rather than escape it. Therefore, Soma and Prozac are not similar. 

Soma is a governmentally provided drug to the people living in the Brave New World.  It represents a way to escape pain, discomfort, embarrassment, sadness or anger and to enhance joy, arousal, and an overall sense of well being.  It is non-addictive (physically or mentally) and has no negative side effects on the mind or body whatsoever.  Individuals are rationed their soma, encouraged to take it, and at times, the soma is used as a means of crowd control in the unlikely situation that a group becomes disorderly.  Clearly the government in the society is using soma to calm and control its citizenry.  Of course, the citizenry is high all the time, so they don't really mind.

Prozac is also a legal drug that is prescribed by doctors to alleviate depression and anxiety.  Its purpose seems to be just like that of soma.  In fact, people have compared the two because many people feel that Prozac is a catch-all type of remedy for everyone and that people are prescribed it when they don't really need it.  Unfortunately, Prozac can be addictive and has been linked to feelings of suicide in some cases.

In both cases, people are being medicated to avoid problems and negative feelings.  This avoidance may lead to negative consequences after all.

Compare and contrast the use of soma in Brave New World with the use of drugs like Prozac in our world.

The other answers have done an excellent job of explaining the medical and technical details of Prozac and soma (to the extent we learn about soma in the novel), so I will step back and address the bigger picture implied in a question that specifically mentions Prozac by name.

The question asks for a comparison of soma use to "drugs like" Prozac, with Prozac as a stand-in for any number of medications that are used as mood enhancers. The bigger picture shows that Huxley was prescient in understanding that advanced industrial societies would turn to widespread medication use to alleviate feelings of sadness and anxiety. "Popping a pill" is done in a widespread way both in our world and in the World State of Brave New World.

In both cases, we could argue (leaving aside the people who truly need the medications) that each culture over-relies on medicating unhappiness rather than addressing the roots causes of it in economic or social terms. If Deltas, for example, routinely need, each and every one, to be handed a soma or half a soma tablet after a work shift, does this not indicate that perhaps there is some problem in the condition of their work that is worth investigating? When does it become easier to hand out a drug than deal with larger social issues? Likewise, we might question not that some people need antidepressants in the US, but why this country, the wealthiest on the planet, prescribes the most antidepressants per capita. But perhaps in both worlds it becomes easier—and more profitable—to give out a medication than to change the conditions of life.

One difference between our world and World State, however, is that there everyone is given soma, whereas even in the US, which has the highest per-capita consumer of anti-depressants in the world, only one in every eleven people is a user. In contrast to the World State, we seem not to desire a society that is one hundred percent reliant on mood-enhancing medications to survive. We are able to tolerate and even see the benefits in asking people to meet with some frustration, unhappiness, and "down" feelings in life, as this is a way for people to learn and grow.

Compare and contrast the use of soma in Brave New World with the use of drugs like Prozac in our world.

Prozac is an antidepressant readily used throughout modern society to treat people suffering from depression, panic attacks, anxiety, or obsessive-compulsive disorders. Prozac is known as a selective serotonin reuptake inhibitors (SSRIs), which increases levels of serotonin in the brain. Serotonin is a chemical that nerve cells produce, which is considered a natural mood stabilizer. Prozac effectively manages the negative symptoms of depression and anxiety by releasing serotonin in the brain and stabilizing one's chemical imbalances.

Similar to Prozac, soma is also a drug that increases pleasurable sensations in the brain and suppresses negative emotions, which is where the similarities end between the two drugs. Unlike Prozac, soma is available to every citizen in Huxley's utopian society and is not used to treat people suffering from depression, panic attacks, or anxiety disorders. Soma also offers people a euphoric feeling, which is similar to a hallucinogen. Citizens use soma as a way to escape from reality and randomly take the narcotic throughout the day. Unlike Prozac, which is a prescription medication, soma is used as a recreational drug and not deemed necessary to recover from a mental illness. The government also uses soma as a tool to placate society by making citizens passive, calm, and comfortable. Essentially, soma is a narcotic that provides users with a euphoric experience while Prozac is a prescribed drug used to increase serotonin levels in the brain so individuals suffering from certain mental illnesses can function.

Compare and contrast the use of soma in Brave New World with the use of drugs like Prozac in our world.

In our modern world, Prozac is used to treat major depressive disorder, anxiety, bulimia, and obsessive-compulsive disorder. Basically, Prozac is an anti-depressant. 

On the other hand, SOMA in the Brave New World is an opiate or opioid. Opiates are naturally extracted from the opium poppy. Opioids, on the other hand, are either manufactured chemically (synthetic) or modified from natural opiates (semi-synthetic). Today, the term "opioids" refer to either synthetic, natural, or semi-synthetic opiates.

Either way, opioids or opiates are narcotic in nature: when taken, they generate a sense of well-being, reducing tension, anxiety, or aggression. Opioids also trigger euphoria, stupor, apathy, and in extreme cases, coma and death. The narcotic nature of opioids like SOMA differ from the anti-depressive nature of a modern drug like Prozac. 

Prozac works by affecting the level of certain neurotransmitters in the brain. For example, it is said that the neurotransmitters serotonin, dopamine, and norepinephrine are associated with depression. A drug such as Prozac is an SSRI (or selective serotonin reuptake inhibitors): it increases the level of serotonin in the brain, as lower levels of serotonin are said to contribute to depression.

So, Prozac differs from SOMA in that it is not meant to induce euphoria or dull the senses. In Brave New World, SOMA is said to be "Christianity without tears." It is also described as "Euphoric, narcotic, pleasantly hallucinant." In Brave New World, SOMA so dulls the senses that the person taking it is unable to recognize the reality of his existence. However, Prozac and SOMA are similar in that they are very effective in reducing symptoms of anxiety and/or depression. 

Compare and contrast the use of soma in Brave New World with the use of drugs like Prozac in our world.

One disturbing similarity in the use of soma in Huxley's novel and the prescribing of anti-depressants in today's society is the intention of keeping people "happy."  Recently, one man wrote a book entitled, In Defense of Unhappiness.  In this book, the author points out that discontent is essential or there will be no productive change in one's life, no growth.  In Huxley's dysutopia people are drugged to keep them from rebelling or desiring any change in their lives, so the the world state will remain as it is.  Likewise, in today's society, people will retain their problems as long as they are not as cognizant of them and are in artificial state of contentment.

Compare and contrast the use of soma in Brave New World with the use of drugs like Prozac in our world.

This is a debatable topic, but certainly some would argue that anti-depressive drugs like prozac are thrown at some people by doctors in exactly the same way that soma is used in this society. Certainly it is not on the same scale, but some would say that anti-depressives are used to stop people facing the realities of life that they need to face. I am not sure if I agree with this, though.

Explain the differences and similarities between soma and prozac from all perspectives (side effects, examples from Brave New World)?

This question has been asked and answered.  Follow the link below.

Compare and contrast the use of soma in Brave New World with the use of the drug like Prozac in our world.

Soma is used in A Brave New World as a drug of instant gratification and a means of escape.  It puts the user into a state of euphoria by dulling their mind and senses.

Similarities to Prozac:

• Users of Soma cease to care about immediate problems.  Anti-depressants have a similar effect of dulling the senses.  When on a Soma trip - characters cannot experience extreme emotions (positive or negative) which is very similar to the effect anti-depressants cause.
• The number of people on anti-depressants is on the rise (especially with the availability of new drugs as well as the fact that it is suddenly socially more acceptable).  Virtually everyone in the book takes Soma.  You could argue that the popularity is somewhat similar.

Differences:

• Prozac (and most other anti-depressants) takes several weeks to build up in the system.  Its effectiveness is based on a regular regimen and unlike Soma does not cause a "high" shortly after consumption.  In this way, Soma is more like an illegal drug (cocaine or marijuana) or even alcohol.
• Soma is used by the government as a method of general control - it aids the brainwashing that is also taking place throughout the novel.  If a drug was ever used in such a capacity today, we would probably consider it dangerous and reminiscent of the holocaust.  In fact, again, marijuana has a similar "brainwashing" effect - and its health risks are still a forerunner for its illegality.

Compare and contrast the use of SOMA in Brave New World with the use of drugs like Prozac in our world.

SOMA was given to the people in Brave New Worldas a reward for doing their jobs well. It kept them calm, peaceful, and happy. Then they couldn't or wouldn't be dissatisfied with the government and its never-ending rules or their petty, repetitive jobs. If they didn't comply, no SOMA. Many anti-depressant drugs have the same general effect except they aren't given away. They must be prescribed and paid for, usually at a pretty high price. We are a drugged up society these days from Ritalin for hyperactive (or noncompliant, energetic kids?) to pain pills and antidepressants. For any ailment, real or imagined, there is a magic pill to keep us happy (?). It also keeps the drug companies in business and wealthy!

Compare and contrast the use of SOMA in Brave New World with the use of drugs like Prozac in our world

Certainly, there is a trend in the U.S. to intervene with people, especially youth, and keep them from being unhappy.  Somehow, somehow parents believe that it is not healthy for children to be unhappy.  This thinking has become so prevalent that one man has written a book in defense of unhappiness, pointing out that all great changes in history have been effected after man's discontent with his conditions.  In addition, the author stats that happiness is dependent upon its counterpart of unhappiness since one can only be happy to the extent that he/she has known sorrow, an intrinsic element of life, as well.

In Brave New World, soma is modeled after a sacred  etheogenic plant in India used for meditation. The plant, now lost, contained halluciogenic properties that produced a euphoric state not dissimilar to anti-depressants.  Like many of the inhabitants of modern society, the people of the New World take soma whenever they are discontent.