EXHIBIT 3.109

BYLAWS

OF

THE EMERGENCY ASSOCIATES FOR MEDICINE, INC.

ARTICLE I

Offices

The principal office shall be in the City of Tampa, County of Hillsborough, and State of Florida.

The corporation may also have offices at such other places both within and without the State of Florida as the Board of Directors may from time to time determine or the business of the corporation may require.

ARTICLE II

Stockholders

Section 1. Annual Meeting. The annual meeting of the stockholders shall be held within the three (3) month period beginning with the first day of the last month of the fiscal year of the corporation for the purpose of electing Directors and for the transaction of such other business as may come before the meeting; the actual day thereof to be set forth in the Notice of Meeting or in the Call and Waiver of Notice of Meeting. If the election of Directors shall not be held at any such annual meeting of the stockholders, or at any adjournment thereof, the Board of Directors shall cause the election to be held at a special meeting of the stockholders as soon thereafter as may be convenient.

Section 2. Special Meetings. Special meetings of the stockholders for any purpose or purposes, unless otherwise prescribed by law or by the Articles of Incorporation, may be called by the President or by the Board of Directors, and shall be called by the President or Secretary at the request in writing of a majority of the Board of Directors then in office, or at the request in writing of stockholders owning not less than one-tenth (1/10th) of the entire capital stock of the corporation issued and outstanding and entitled to vote thereat. Such request shall state the purpose or purposes of the proposed meeting. Business transacted at any special meeting of stockholders shall be limited to the purposes stated in the notice thereof.

Section 3. Place of Meeting. The Board of Directors may designate any place either within or without the State of Florida, unless otherwise prescribed by law or by the Articles of Incorporation, as the place of meeting for any annual meeting or for any special meeting of the stockholders. A waiver of notice signed by all stockholders entitled to vote at a meeting may designate any place either within or without the State of Florida, unless otherwise prescribed by law or by the Articles of Incorporation, as the place for the holding of such meeting. If no designation is made or if a special meeting be otherwise called, the place of meeting shall be the principal office of the corporation in the State of Florida.

Section 4. Notice of Meeting. Written or printed notice stating the place, day and hour of the meeting, and in the case of a special meeting, the purpose or purposes for which the meeting is called shall be delivered not less than ten (10) nor more than sixty (60) days before the date of the meeting, either by hand delivery, express or other delivery service, telecopier, telegram, telex, mailgram, cablegram or other delivery method or by first-class mail, by or at the direction of the President or the Secretary, or the officer or persons calling the meeting, to each stockholder of record entitled to vote at such meeting. If mailed, such notice shall be deemed to be delivered when deposited in the United States mail, addressed to the stockholder at his business or home address of the stockholder’s address as it appears on the stock transfer books of the corporation, with postage thereon prepaid.

Section 5. Waiver of Notice of Meeting. Whenever any notice to a stockholder is required pursuant to the provisions of Section 4 hereinabove, each stockholder may waive such notice in writing at any time before or after the time for the delivery of such notice, and such written waiver of notice shall be equivalent to the giving of such notice. Attendance at any meeting by any stockholder to whom notice of such meeting must be given pursuant to the provisions of Section 4 hereinabove shall constitute a waiver of notice of such meeting by such stockholder, except when the stockholder attends such meeting for the express purpose of objecting, at the beginning of the meeting, to the transaction of any business at the meeting because the meeting is not lawfully called or convened.

Section 6. Voting Lists. The officer or agent having charge of the stock transfer books for shares of the corporation shall make, at least ten (10) days before each meeting of stockholders, a complete list of the stockholders entitled to vote at such meeting or any adjournment thereof arranged in alphabetical order, with the address and the number and class and series of shares held by each; which list, for a period of ten (10) days prior to such meeting, shall be kept on file at the principal office of the corporation and shall be subject to inspection of any stockholder during the whole time of the meeting. The original stock transfer book shall be prima facie evidence as to who are the stockholders entitled to examine such list or transfer books or to vote at any meeting of the stockholders.

Section 7. Quorum. A majority of the outstanding shares of the corporation entitled to vote, represented in person or by proxy, shall constitute a quorum at a meeting of stockholders, unless otherwise provided in the Articles of Incorporation, but in no event shall a quorum consist of less than one-third (1/3) of the shares entitled to vote at the meeting. If less than a majority of the outstanding shares are represented at a meeting, a majority of the shares so represented may adjourn the meeting from time to time without further notice. At such adjourned meeting at which a quorum shall be present or represented, any business may be transacted which might have been transacted at the meeting as originally notified. The stockholders present at a duly organized meeting may continue to transact business until adjournment, notwithstanding the withdrawal of enough stockholders to leave less than a quorum.

Section 8. Voting of Shares. Each stockholder entitled to vote shall at every meeting of the stockholders be entitled to one (1) vote in person or by proxy, signed by him, for each share of the voting stock held by him that has been transferred on the books of the corporation prior to such meeting. Such right to vote shall be subject to the right of the Board of Directors to close the transfer books or to fix a record date for voting stockholders pursuant to the provisions of Article VIII hereinafter.

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Section 9. Proxies. At all meetings of stockholders, a stockholder may vote by proxy, executed in writing by the stockholder or by his duly authorized attorney-in-fact; but no proxy shall be valid after eleven (11) months from its date, unless the proxy provides for a longer period. Such proxies shall be filed with the Secretary of the corporation before or at the time of the meeting.

Section 10. Informal Action by Stockholders.

(a) Any action which may be taken or is required by law to be taken at any annual or special meeting of the stockholders may be taken without a meeting and without a vote, if a consent in writing, setting forth the action so taken, shall be signed by the holders of a majority of the outstanding stock of the corporation. If any class of stock is entitled to vote thereon as a class, such written consent shall be required of the holders of a majority of the stock of each class of stock entitled to vote as a class thereon and of the total stock entitled to vote thereon.

(b) Unless all of the holders of the outstanding stock of the corporation have signed a written consent to an action in accordance with the provisions of paragraph (a) hereinabove, then within ten (10) days after obtaining such written consent notice must be given to those stockholders who have not so consented in writing. The notice shall fairly summarize the material features of the authorized action, and, if the action be a merger, consolidation, or sale or exchange of assets for which dissenters’ rights are provided by Florida law, the notice shall contain a clear statement of the right of stockholders dissenting therefrom to be paid the fair value of their shares upon compliance with Florida law regarding the rights of dissenting stockholders.

ARTICLE III

Board of Directors

Section 1. General Powers. The business and affairs of the Corporation shall be managed by its Board of Directors.

Section 2. Number, Tenure and Qualifications. The number of directors of the corporation shall be not less than one (1), nor more than fifteen (15); the number of the same to be fixed by the stockholders at any annual or special meeting. Each Director shall hold office until the next annual meeting of stockholders or until his successor has been elected, unless sooner removed by the stockholders at any general or special meeting. None of the Directors need be residents of the State of Florida.

Section 3. Annual Meeting. After each annual meeting of stockholders, the Board of Directors shall hold its annual meeting at the same place as and immediately following such annual meeting of stockholders for the purpose of the election of officers and the transaction of such other business as may come before the meeting; and if a majority of the Directors be present at such place and time, no prior notice of such meeting shall be required to be given to the Directors. The place and time of such meeting may also be fixed by written consent of the Directors.

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Section 4. Regular Meetings. Regular meetings of the Board of Directors may be held without notice at such time and at such place as shall be determined from time to time by the Board of Directors.

Section 5. Special Meetings. Special meetings of the Board of Directors may be called by the Chairman of the Board, if there be one, or the President or any two (2) Directors. The person or persons authorized to call special meetings of the Board of Directors may fix the place, time and date for holding any special meetings of the Board of Directors called by them.

Section 6. Notice of Meeting or Waiver Thereof. Notice of any special meeting shall be given at least two (2) days prior thereto by written notice delivered personally or mailed to each Director at his business or home address. If mailed, such notice shall be deemed to be delivered when deposited in the United States mail so addressed with postage thereon prepaid. If notice be given by telegram, such notice shall be deemed to be delivered when the telegram is delivered to the telegraph company. If notice is given by cablegram, such notice shall be deemed to be delivered when the cablegram is dispatched. Any Director may waive notice of such meeting either before, at or after such meeting. The attendance of a Director at a meeting shall constitute a waiver of notice of such meeting, except where a Director attends a meeting for the express purpose of objecting to the transaction of any business because the meeting is not lawfully called or convened. Notice need not specify the purpose of any meeting.

Section 7. Quorum. A majority of the Directors shall constitute a quorum, but a smaller number may adjourn from time to time without further notice until a quorum is secured.

Section 8. Manner of Acting. The act of a majority of the Directors voting for or against, (disregarding any abstentions) at a meeting at which a quorum is present shall be the act of the Board of Directors.

Section 9. Vacancies. Any vacancy occurring in the Board of Directors, including any vacancy created by reason of an increase in the number of Directors, may be filled by the affirmative vote of a majority of the remaining Directors, though less than a quorum of the Board of Directors. A Director elected to fill a vacancy shall be elected for the unexpired term of his predecessor in office.

Section 10. Compensation. By resolution of the Board of Directors, the Directors may be paid their expenses, if any, of attendance at each meeting of the Board of Directors, and may be paid a fixed sum for attendance at each meeting of the Board of Directors, or a stated salary as Directors. No payment shall preclude any Director from serving the corporation in any other capacity and receiving compensation therefor.

Section 11. Presumption of Assent. A Director who is present at a meeting at which action on any corporate matter is taken shall be presumed to have assented to the action taken, unless he votes against such action or abstains from voting in respect thereto. A Director may abstain from voting on any matter in his sole discretion.

Section 12. Informal Action by Board. Any action required or permitted to be taken by any provisions of law, of the Articles of Incorporation or these bylaws at any meeting of the Board of

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Directors or of any committee thereof may be taken without a meeting if, prior to such action, a written consent thereto is signed by all members of the Board or of such committee, as the case may be, setting forth the actions so to be taken and filed in the minutes of the proceedings of the Board or of the committee.

Section 13. Telephonic Meetings. Members of the Board of Directors or an executive committee shall be deemed present at a meeting of such Board or committee if a conference telephone, or similar communications equipment, by means of which all persons participating in the meeting can hear each other at the same time, is used.

Section 14. Removal. Any director may be removed, with or without cause, by the stockholders at any general or special meeting of the stockholders whenever, in the judgment of the stockholders, the best interest of the corporation will be served thereby, but such removal shall be without prejudice to the contract rights, if any, of the person removed. This bylaw shall not be subject to change by the Board of Directors.

ARTICLE IV

Officers

Section 1. Number. The officers of the corporation shall be a President, a Secretary and a Treasurer, each of whom shall be elected by the Board of Directors. The Board of Directors may also elect a Chairman of the Board, one or more Vice Presidents, one or more Assistant Secretaries and Assistant Treasurers and such other officers as the Board of Directors shall deem appropriate. Any two (2) or more offices may be held by the same person.

Section 2. Election and Term of Office. The officers of the corporation shall be elected annually by the Board of Directors at its first meeting after each annual meeting of stockholders. If the election of officers shall not be held at such meeting, such election shall be held as soon thereafter as may be convenient. Each officer shall hold office until his successor shall have been duly elected and shall have qualified or until his death or until he shall resign or shall have been removed in the manner hereinafter provided.

Section 3. Removal. Any officer elected or appointed by the Board of Directors may be removed by the Board of Directors whenever, in its judgment, the best interest of the corporation will be served thereby, but such removal shall be without prejudice to the contract rights, if any, of the person so removed.

Section 4. Vacancies. A vacancy in any office because of death, resignation, removal, disqualification or otherwise, may be filled by the Board of Directors for the unexpired portion of the term.

Section 5. Duties of Officers. The Chairman of the Board of the corporation, or the President if there shall not be a Chairman of the Board, shall preside over all meetings of the Board of Directors and of the stockholders, which he shall attend. The President shall be the chief executive officer of the corporation. Subject to the foregoing, the officers of the corporation shall have such powers and duties as usually pertain to their respective offices and such additional powers and duties

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specifically conferred by law, by the Articles of Incorporation, by these bylaws, or as may be assigned to them from time to time by the Board of Directors.

Section 6. Salaries. The salaries of the officers shall be fixed from time to time by the Board of Directors, and no officer shall be prevented from receiving such salary by reason of the fact that he is also a Director of the corporation.

Section 7. Delegation of Duties. In the absence of or disability of any officer of the corporation or for any other reason deemed sufficient by the Board of Directors, the Board may delegate his powers or duties to any other officer or to any other Director for the time being.

ARTICLE V

Executive and Other Committees

Section 1. Creation of Committees. The Board of Directors may, by resolution passed by a majority of the whole Board, designate an Executive Committee and one (1) or more other committees, each to consist of one (1) or more of the Directors of the corporation.

Section 2. Executive Committee. The Executive Committee, if there shall be one, shall consult with and advise the officers of the corporation in the management of its business and shall have and may exercise, to the extent provided in the resolution of the Board of Directors creating such Executive Committee, such powers of the Board of Directors as can be lawfully delegated by the Board.

Section 3. Other Committees. Such other committees shall have such functions and may exercise the powers of the Board of Directors, as can be lawfully delegated, and to the extent provided in the resolution or resolutions creating such committee or committees.

Section 4. Meetings of Committees. Regular meetings of the Executive Committee and other committees may be held without notice at such time and at such place as shall from time to time be determined by the Executive Committee or such other committees, and special meetings of the Executive Committee or such other committees may be called by any member thereof upon two (2) days’ notice to each of the other members of such committee; or on such shorter notice as may be agreed to in writing by each of the other members of such committee, given either personally or in the manner provided in Section 6 of Article III of these bylaws (pertaining to notice for Directors’ meetings).

Section 5. Vacancies on Committees. Vacancies on the Executive Committee or on such other committees shall be filled by the Board of Directors then in office at any regular or special meeting.

Section 6. Quorum of Committees. At all meetings of the Executive Committee or such other committees, a majority of the committee’s members then in office shall constitute a quorum for the transaction of business.

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Section 7. Manner of Acting of Committees. The acts of a majority of the members of the Executive Committee or such other committees present at any meeting at which there is a quorum shall be the act of such committee.

Section 8. Minutes of Committees. The Executive Committee, if there shall be one, and such other committees shall keep regular minutes of their proceedings and report the same to the Board of Directors when required.

Section 9. Compensation. Members of the Executive Committee and such other committees may be paid compensation in accordance with the provisions of Section 10 of Article III (pertaining to compensation of Directors).

ARTICLE VI

Indemnification and Advancement of Expenses for Directors, Officers, Employees and Agents

The corporation shall indemnify and advance expenses to any person who was or is a party to any proceeding or threatened proceeding by reason of the fact that he is or was a director, officer, employee, or agent of the corporation or is or was serving at the request of the corporation; subject in each instance to satisfaction of all applicable requirements under Chapter 607, Florida Statutes.

Additionally, the corporation may make any other or further indemnification or advancement of expenses of any of its directors, officers, employees, or agents, as it may desire, subject, however, to the restrictions contained in Chapter 607, and in particular Section607.014(7), Florida Statutes.

ARTICLE VII

Certificates of Stock

Section 1. Certificates for Shares. Every holder of stock in the corporation shall be entitled to have a certificate signed by the President or a Vice President and the Secretary or an Assistant Secretary exhibiting the holder’s name and certifying the number of shares owned by him in the corporation. The certificates shall be numbered and entered in the books of the corporation as they are issued.

Section 2. Transfer of Shares. Transfers of shares of the corporation shall be made upon its books by the holder of the shares in person or by his lawfully constituted representative upon surrender of the certificate of stock for cancellation. The person in whose name shares stand on the books of the corporation shall be deemed by the corporation to be the owner thereof for all purposes, and the corporation shall not be bound to recognize any equitable or other claim to or interest in such shares on the part of any other person whether or not it shall have express or other notice thereof, save as expressly provided by the laws of the State of Florida.

Section 3. Facsimile Signature. Where a certificate is manually signed on behalf of a transfer agent or a registrar other than the corporation itself or an employee of the corporation, the signature of any such President, Vice President, Secretary or Assistant Secretary may be a facsimile.

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In case any officer or officers who have signed or whose facsimile signature or signatures shall cease to be such officer or officers of the corporation, such certificate or certificates may, nevertheless, be adopted by the corporation and be issued and delivered as though the person or persons who signed such certificate or certificates or whose facsimile signature or signatures have been used thereon had not ceased to be such officer or officers of the corporation.

Section 4. Lost Certificates. The Board of Directors may direct that a new certificate or certificates be issued in place of any certificate or certificates theretofore by the corporation and alleged to have been lost or destroyed, upon the making of an affidavit of that fact by the person claiming the certificate of stock to be lost or destroyed. When authorizing such issue of a new certificate or certificates, the Board of Directors may, in its discretion and as a condition precedent to the issuance thereof, require the owner of such lost or destroyed certificate or certificates or his legal representative to advertise the same in such manner as it shall require and/or to give the corporation a bond in such sum as it may direct as indemnity against any claim that may be made against the corporation with respect to the certificate alleged to have been lost or destroyed.

ARTICLE VIII

Record Date

The Board of Directors is authorized from time to time to fix in advance a date, not more than sixty (60) nor less than ten (10) days before the date of any meeting of stockholders, or not more than sixty (60) days prior to the date for the payment of any dividend or the date for the allotment of rights, or the date when any change or conversion of or exchange of stock shall go into effect, or a date in connection with the obtaining of the consent of stockholders for any purpose, as a record date for the determination of the stockholders entitled to notice of and to vote at any such meeting and any adjournment thereof, or entitled to receive payment of any such dividend, or to any such allotment, or to exercise the rights in respect of any such change, conversion or exchange of stock, or to give such consent, as the case may be; and, in such case, such stockholders and only such stockholders as shall be stockholders of record on the date so fixed shall be entitled to such notice of and to vote at such meeting and any adjournment thereof, or to receive payment of such dividend, or to receive such allotment of rights, or to exercise such rights, or to give such consent, as the case may be, notwithstanding any transfer of any stock on the books of the corporation after any such record date fixed as aforesaid.

ARTICLE IX

Dividends

The Board of Directors may from time to time declare and the corporation may pay dividends on its outstanding shares of capital stock in the manner and upon the terms and conditions provided by the Articles of Incorporation and by law. Dividends may be paid in cash, in property or in shares of stock, subject to the provisions of the Articles of Incorporation and to law.

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ARTICLE X

Fiscal Year

The fiscal year of the corporation shall be the twelve month period selected by the Board of Directors as the taxable year of the corporation for federal income tax purposes.

ARTICLE XI

Seal

The corporate seal shall bear the name of the corporation, which shall be between two concentric circles, and in the inside of the inner circle shall be the calendar year of incorporation; an impression of said seal appearing on the margin hereof.

ARTICLE XII

Stock in Other Corporations

Shares of stock in other corporations held by this corporation shall be voted by such officer or officers of this corporation as the Board of Directors shall from time to time designate for the purpose, or by a proxy thereunto duly authorized by said Board.

ARTICLE XIII

Amendments

These bylaws may be altered, amended, or repealed in whole or in part, and new bylaws may be adopted by the Board of Directors or by the vote of stockholders owning a majority of the stock of the corporation entitled to vote thereon.

ARTICLE XIV

Restrictions on Stock

Section 1. Restrictions. Except as hereinafter provided in Sections 4 and 6, no owner of stock in the corporation or of an interest in such stock, whether legal or equitable, and whether such owner be an individual, fiduciary, corporation or other entity, may sell, exchange or otherwise dispose of any such stock or interest therein during his or her lifetime without the written consent of the corporation and each of the stockholders of the corporation, or, in the absence of such written consent, without first offering such stock or interest therein to the corporation at the same price and upon the same terms and conditions that said stockholder desires to sell, exchange or otherwise dispose of such stock or interest therein. The corporation shall have a period of thirty (30) days after receiving notice of such offer within which to accept such offer; and if such offer is not accepted by the corporation within said thirty (30) day period, then the said offer shall be made to the other owners of stock of the corporation, exercisable by each in proportion to the stock of the corporation (excluding the stock of

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the selling stockholder) owned by each. The stockholder to whom such offer is made shall have a period of thirty (30) days thereafter in which to accept such offer.

Section 2. Term of Restrictions. The restrictions contained in the foregoing paragraph shall be continuing restrictions applicable at all times to the outstanding stock of the corporation, and no action by the corporation shall be deemed to have freed any stock of the corporation or interest therein from such restrictions, and all subsequent owners of such stock shall take same subject to these restrictions.

Section 3. Legend on Stock Certificates. All certificates of stock of the corporation shall bear the following endorsement:

Neither the capital stock represented by this certificate nor any interest therein may be sold, exchanged or otherwise disposed of unless the restrictions and provisions contained in Article XIV of the bylaws of the corporation are first complied with. A copy of said Article XIV may be obtained at the office of the corporation.

Section 4. Absence of Restrictions on Certain Gratuitous Transfers of Stock. Except as provided in any written agreement entered into by the corporation and its stockholders pursuant to Section 6 hereinafter, there shall be no restriction whatsoever on any gratuitous transfer of stock by an individual stockholder during his or her lifetime to or for the benefit of his or her spouse, lineal descendants or lineal ascendants; provided, however, that any recipient of stock in the corporation pursuant to a gratuitous transfer in accordance with this Section 4 shall receive such stock subject to the restrictions imposed by this Article XIV and shall be bound by all the terms, duties and obligations imposed by this Article XIV.

Section 5. Negation of Restriction on Transfer of Stock Upon Death. This Article XIV does not impose any restriction upon a testamentary transfer of stock in the corporation by an individual stockholder or upon transfer of stock in the corporation pursuant to applicable laws of intestate succession; provided, however, that any recipient of stock in the corporation pursuant to a transfer from a deceased stockholder in accordance with this Section 5 shall receive such stock subject to the restrictions imposed by this Article XIV and shall be bound by all the terms, duties and obligations imposed by this Article XIV.

Section 6. Stock Restriction Agreement Among Stockholders. The stockholders of the corporation may further implement this Article XIV by entering into a written agreement among themselves providing for more specific terms (including a different purchase price) and conditions for the sale of the stock of a stockholder during his lifetime or upon his death; and, in such event, the terms (including purchase price) and conditions of sale set forth in such written agreement shall be controlling and shall take precedence over the foregoing provisions of this Article XIV; provided, that in no event shall this Section 6 be applied unless such agreement between the stockholders shall have been entered into by all the stockholders to which this Article XIV is applicable and the corporation shall have consented or been a party thereto.

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ARTICLE XV

Reimbursement of Disallowed Expenses

Any payments made to an officer of the corporation such as salary, commission, bonus, interest or rent or for entertainment expenses incurred by him which shall be disallowed in whole or in part as a deductible expense by the Internal Revenue Service shall be reimbursed by such officer to the corporation to the full extent of such disallowance. It shall be the duty of the Directors, as a Board, to enforce payment of each such amount disallowed. Reimbursement of such disallowed amounts may, subject to the determination of the Directors, be withheld in proportionate amounts from the future compensation payments of the officer until the amount owed to the corporation has been recovered.

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