<PAGE>   1
                                                                   EXHIBIT 10.13

SHAREHOLDERS AGREEMENT entered into as of the 4th day of February, 2000.



BETWEEN  INFECTIO DIAGNOSTIC (I.D.I.) INC., a corporation incorporated under the
         laws of the Province of Quebec ("IDI")



AND      CEPHEID, a corporation incorporated under the laws of the state of
         California ("Cepheid")



AND      ARIDIA CORP., a corporation incorporated under the laws of the Province
         of Nova Scotia ("Corporation")



WHEREAS the Corporation is a company incorporated under the Nova Scotia
Companies Act by Certificate of Incorporation dated the 4th day of February,
2000, and is qualified as a Nova Scotia Unlimited Liability Company;

WHEREAS the share capital of the Corporation consists of a limited number of
1,000,000 common shares of which 200 common shares have been issued and are
presently outstanding and registered as follows:


<TABLE>
<CAPTION>

               NAME                                       COMMON SHARES
               ----                                       -------------
              <S>                                         <C>
               IDI                                             100

               Cepheid                                         100
</TABLE>



WHEREAS IDI and the Corporation have entered concurrently with the execution of
this Agreement into a License and Supply Agreement;

WHEREAS Cepheid and the Corporation have entered concurrently with the execution
of this Agreement into a License and Supply Agreement;

WHEREAS the parties wish to enter into this Agreement in order to record their
mutual understanding as to the manner in which the affairs of the Corporation
shall be conducted and to provide for their respective rights and obligations;

NOW THEREFORE, in consideration of the mutual covenants and agreements
hereinafter set forth and other good and valuable consideration, the parties
hereby agree as follows:


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                                    ARTICLE 1

                                 INTERPRETATION



1.1   DEFINITIONS

      The capitalized words and expressions used in this Agreement or in its
      Schedules, or in any deed or agreement supplemental or ancillary hereto,
      unless there be something in the subject or the context inconsistent
      therewith, shall have the meanings respectively:

      "AFFILIATE" shall mean any corporation or other business entity controlled
      by or in common Control of a party. "Control" as used herein means
      ownership directly or through one or more Affiliates, of fifty percent
      (50%) or more of the shares of the share capital entitled to vote for the
      election of directors, in the case of any corporation, or fifty percent
      (50%) or more of the equity interests in the case of any other type of
      legal entity, status as a general partner in any partnership, or any other
      arrangement whereby a party controls or has the right to control the board
      of directors or equivalent governing body of a corporation other entity.

      "AUDITORS" means the auditors of the Corporation appointed pursuant to the
      provisions of Section 3.6 hereof;

      "BOARD" means the board of directors of the Corporation;

      "BUSINESS DAY" means any day excluding Saturday, Sunday and any other day
      which in the city of Quebec, Canada or in the State of California is a
      legal holiday or a day on which financial institutions are authorized by
      law or by local proclamation to close;

      "CEPHEID DIRECTOR" means the Directors appointed pursuant to the
      provisions of subsection 3.2.1 hereof;

      "CEPHEID LICENSE" means the License and Supply Agreement between Cepheid
      and the Corporation dated February 4, 2000;

      "COLLABORATION AGREEMENT" means the Joint Technology and Collaboration
      Agreement between IDI, Cepheid and the Corporation dated February 4, 2000;

      "CONTROL" means ownership directly or through one or more Affiliates, of
      fifty percent (50%) or more of the shares of the share capital entitled to
      vote for the election of directors, in the case of any corporation, or
      fifty percent (50%) or more of the equity interests in the case of any
      other type of legal entity, status as a general partner in any
      partnership, or any other arrangement whereby a party controls or has the
      right to control the board of directors or equivalent governing body of a
      corporation or other entity;

      "DIRECTOR" or "DIRECTORS" means a member or the members of the Board;

      "EFFECTIVE DATE" means February 4, 2000;

      "FISCAL YEAR" shall have the meaning ascribed to such term in Section
      3.2.8 hereof;


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                                      -3-


      "HEADS OF AGREEMENT" means the Heads of Agreement between IDI and Cepheid
      dated August 5, 1999;

      "IDI DIRECTORS" means the directors appointed pursuant to the provisions
      of subsection 3.2.1 hereof;

      "IDI LICENSE" means the License and Supply Agreement between IDI and the
      Corporation dated February 4, 2000;

      "LIEN" means any interest in property or the income or profits therefrom
      securing an obligation owed to, or a claim by, a Person other than the
      owner (which for the purposes hereof shall include a possessor under a
      title retention agreement and a lessee under a lease hereinbelow
      described) of such property, whether such interest is based on civil law,
      common law, statute or contract, and including but not limited to any
      security interest, hypothec, mortgage, pledge, lien, claim, charge,
      cession, transfer, assignment, encumbrance, title retention agreement,
      lessor's interest under a lease which would be capitalized on a balance
      sheet of the owner of such property or analogous interest in, of or on any
      property or the income or profits therefrom of a Person;

      "PERSON OR PERSON" means any individual, company, corporation,
      partnership, firm, trust, sole proprietorship, government or entity
      howsoever designated or constituted;

      "SHARES" means shares in the share capital of the Corporation which have
      been issued and are outstanding at any time and from time to time;

      "SHAREHOLDERS" means the parties to this Agreement and each Person to whom
      any Shares may at any time and from time to time be issued, each
      transferee of Shares and the respective representatives, administrators,
      successors and assigns of each of the above-mentioned Persons;

      "THIS AGREEMENT", the "AGREEMENT", "HERETO", "HEREIN", "HEREBY",
      "HEREUNDER" and similar expressions mean or refer to this Shareholders
      Agreement as amended from time to time and any indenture, agreement or
      instrument supplemental or ancillary hereto or in implementation hereof,
      and the expressions "SECTION", "SUBSECTION" and "CLAUSE" followed by a
      number or letter mean and refer to the specified section, subsection or
      paragraph of this Agreement;

1.2   GENERAL INTERPRETATION

      Unless there be something in the subject or the context inconsistent
      therewith, words importing the singular only shall include the plural and
      vice versa, and words importing the masculine gender shall include the
      feminine gender, and vice versa, and all references to dollars shall mean
      Canadian dollars, the legal currency of Canada.

1.3   DIVISION INTO ARTICLES

      The division of this Agreement into articles, sections, subsections,
      paragraphs and subparagraphs and the insertion of titles are only meant to
      be reference and do not affect the meaning or the interpretation of this
      Agreement.


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                                      -4-


1.4   ACCOUNTING PRINCIPLES

      All calculations required to be made under the terms hereof and all
      financial statements shall be prepared in accordance with the generally
      accepted accounting principles applied in Canada on a consistent basis.

1.5   GOVERNING LAW

      This Agreement and the interpretation and enforcement thereof shall be
      governed by the laws of the Province of Quebec without regard to any
      conflicts of law principles and the federal laws of Canada applicable
      therein.


                                    ARTICLE 2

                           PURPOSE OF THE CORPORATION



2.1   PURPOSE OF THE CORPORATION

      The Corporation was created by IDI and Cepheid in order to engage
      primarily in the business of developing, producing and exploiting a series
      of innovative human diagnostic systems and products for rapid
      identification of pathogens responsible for human infectious diseases
      based on the integration of proprietary technologies of IDI and Cepheid.




                                    ARTICLE 3

                 ORGANIZATION AND MANAGEMENT OF THE CORPORATION



3.1   SHAREHOLDERS

      The Shareholders shall each vote all Shares from time to time held by each
      of them and otherwise exercise their rights as Shareholders and, to the
      extent permitted by applicable law, cause their respective nominees to the
      Board to act, so that at all times the general provisions of the by-laws
      and the conditions, restrictions, limitations and prohibitions on the
      business and corporate affairs of the Corporation set forth in this
      Agreement shall apply and be given full effect.

3.2   GENERAL BY-LAWS

      The Articles of Association of the Corporation shall provide for the
      following continuing provisions with respect to the organization and
      management of the Corporation:

      3.2.1 Number of Directors

            The Board shall consist of 6 Directors who shall be nominated and
            elected as follows:

            (a)   IDI shall be entitled to nominate and have elected 3 Directors
                  (the "IDI Directors"); and

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                                      -5-




            (b)   Cepheid shall be entitled to nominate and have elected 3
                  Directors (the "Cepheid Directors").

      3.2.2 Meetings of Directors

            Subject to the provisions of applicable law, the following
            procedures shall apply to meetings of Directors of the Corporation

            (a)   Regular meetings of the Board shall be held at least 4 times
                  per year, with a minimum period of 2 months and a maximum
                  period of 3 months between each meetings. Other meetings of
                  the Board shall be held at such time as may be requested by
                  any Director;

            (b)   A meeting of the Board may be called by any Director, provided
                  at least 3 Business Days prior written notice is sent to all
                  Directors. A Director may waive notice of a meeting of the
                  Board, and the attendance of a Director at a meeting shall
                  constitute a waiver of notice of the meeting (except where a
                  Director attends a meeting for the express purpose of
                  objecting to the transaction of business on the grounds that
                  the meeting is not properly called) Meetings may be held by
                  conference telephone call;

            (c)   A quorum of a meeting of the Board shall consist of 6
                  Directors;

      3.2.3 Unanimous Vote to Govern - Directors' Meetings

            All decisions of the Board shall be decided by the unanimous vote of
            all the Directors present in person.

      3.2.4 Ostensible Authority

            No officer or Director of the Corporation may enter into any
            contract for or on behalf of the Corporation which involves the
            payment or obligation by the Corporation of an aggregate amount in
            excess of $10,000, or has an aggregate term (including any renewal
            term or extended term) of more than 12 months, without the prior
            approval of the Board, evidenced by resolution of the said Board.
            The Shareholders shall take the appropriate measures to ensure that
            the officers and the Directors of the Corporation comply with this
            provision.

      3.2.5 Business transaction

            Until any vacancy on the Board is filled in accordance with Section
            3.4, the Directors shall not transact any business.

      3.2.6 Meetings of Shareholders

            A meeting of the Shareholders may be called by the Board, provided
            at least 10 Business Days prior written notice is sent to the
            Shareholders. A Shareholder may waive notice of a meeting of the
            Shareholders, and the attendance of a Shareholder at a meeting shall
            constitute a waiver of notice of the meeting (except where a
            Shareholder attends a meeting for the express purpose of objecting
            to the transaction of business on the grounds that the meeting is
            not properly called).



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      3.2.7 Quorum of Meetings of Shareholders

            A quorum of a meeting of the Shareholders of the Corporation shall
            consist of all the Shareholders.

      3.2.8 Fiscal Year

            The fiscal year end of the Corporation shall be December 31 of each
            year.

      3.2.9 Amendment or repeal

            The Directors shall not make, amend or repeal any by-laws except if
            the Shareholders have unanimously voted for such by-law, amendment
            or repeal.

3.3   FIRST DIRECTORS

      The first IDI Directors shall be:

      Dr. Michel. G. Bergeron
      Dr. Pierre Coulombe
      Mr. Jacques Millette


      and the first Cepheid Directors shall be:

      Mr. Thomas L. Gutshall
      Mr. Cris McReynolds
      Dr. Kurt Petersen.

3.4   ELECTION, REMOVAL AND VACANCIES

      The Shareholders shall each vote the Shares from time to time held by each
      of them and otherwise exercise their rights to ensure that Directors are
      elected or appointed and maintained in office and vacancies on the Board
      are filled in conformity with the provisions of Section 3.2.1 hereof. Each
      of the Shareholders shall have the right to remove any Director previously
      proposed by it and, if requested to do so, the other Shareholder shall
      vote the Shares from time to time held by it for the removal of any such
      Director and in favor of any substitute proposed by the Shareholder
      requesting such removal.

3.5   OFFICERS

      The officers of the Corporation shall be:

      Dr. Pierre Coulombe                 President
      Mr. Thomas L. Gutshall              Chairman of the Board
      Mr. Francois Duchesneau             Secretary

      and such other officers as may be appointed from time to time by the
      Board. The officers of the Corporation shall be appointed annually.

3.6   AUDITOR

      PricewaterhouseCoopers LLP shall be the auditors of the Corporation. Each
      of the Shareholders may from time to time request the auditors to perform,
      at the cost of such Shareholder, accounting and auditing tasks in addition
      to those functions that the auditors would ordinarily perform.


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3.7   ACCOUNTING

      The books of account and all other financial records of the Corporation
      shall be kept and maintained at all times at the principal business office
      of the Corporation in the Province of Quebec. The Shareholders, or their
      agents, representatives and employees, shall be entitled to have access to
      and inspect all such books and records during normal business hours. They
      shall also be entitled, at their own expense, to obtain copies of such
      books and records.

3.8   CORPORATION

      The Corporation agrees to carry out and be bound by the provisions of this
      Agreement as it applies to it to the fullest extent permitted by law.

3.9   UNITED STATES TAX STATUS

      The Corporation shall make any election requested by Cepheid regarding its
      status as a corporation or a partnership for United Sates tax purposes.


                                    ARTICLE 4

               RESTRICTIONS ON TRANSFER OF SHARES AND EXIT RIGHTS

4.1   GENERAL RESTRICTION ON TRANSFER

      No Shareholder may sell, transfer, alienate or otherwise dispose or divest
      itself of or create, incur, assume or suffer to exist any Lien on all or
      part of its Shares except in conformity with the provisions of this
      Article 4.

4.2   EXIT RIGHTS

      Each of the Shareholders (the "Petitioner") shall be entitled at any time
      after 18 months after the Effective Date to send a written notice to the
      other Shareholder and the Corporation requesting the winding up of the
      Corporation (the "Winding up Notice"). The Shareholders and the
      Corporation agree in advance that the winding up of the Corporation shall
      be effective 6 months after the receipt by the other Shareholder and the
      Corporation of the Winding up Notice.

4.3   EFFECT OF WINDING UP NOTICE

      Upon the receipt by the other Shareholder and the Corporation of a Winding
      up Notice, the other Shareholder and the Corporation shall have 30 days to
      notify in writing the Petitioner that they will collaborate to wind up the
      Corporation, in which case the winding up of the Corporation shall be
      effective 180 days after receipt of the Winding up Notice.

      4.3.1 Rules of voluntary winding up

            If the other Shareholder and the Corporation have agreed to
            collaborate to voluntary wind up the Corporation, the following
            rules shall apply:

            (a)   The Shareholders and the Corporation shall take all acts
                  necessary or useful to voluntary wind up the Corporation
                  within 180 days after the receipt of the Winding up Notice.



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            (b)   The Corporation shall carry on business until 180 days after
                  receipt by a Shareholder and the Corporation of the Winding up
                  Notice. At the expiration of the 180 day period, the
                  Corporation shall cease to carry on business except to the
                  extent necessary for the finalization of the winding up of the
                  Corporation.

            (c)   During the 180 day period, the Corporation shall take all
                  appropriate measures to complete the sale of any Collaborative
                  Products and Products to third party pursuant to any then
                  outstanding agreements and the Shareholders agree to negotiate
                  in good faith to restructure any agreements to which the
                  Corporation was a party for the distribution and sale of the
                  Collaborative Products and Products or to put in place new
                  agreements to enable continued supply of the Collaborative
                  Products and Products sold by the Corporation to a third party
                  distributor after the Corporation has ceased to carry on
                  business.

      4.3.2 Expiration of the 180 day period

            At the expiration of the 180 day period:

            (a)   The Corporation shall cease to use IDI Intellectual Property
                  and Cepheid Intellectual Property.

            (b)   IDI shall have a fully paid-up, worldwide license under
                  Cepheid Intellectual Property to use, offer to sell and sell
                  products based upon Cepheid Intellectual Property in the
                  Field, which license shall be in conformity with the terms and
                  conditions of the Cepheid License.

            (c)   Cepheid shall have a fully paid-up worldwide license under IDI
                  Intellectual Property to use, offer to sell and sell products
                  based upon IDI Intellectual Property in the Field, which
                  license shall be in conformity with the terms and conditions
                  of the IDI License.

            (d)   Cepheid and IDI will negotiate in good faith for supply
                  agreements pursuant to which IDI would supply Cepheid with IDI
                  Products and Cepheid would supply IDI with Cepheid Products.

4.4   APPLICATION TO THE COURT

      If the other Shareholder and/or the Corporation have (i) failed within the
      30 day period set forth in Subsection 4.3.1 to notify the Petitioner that
      they will collaborate in the winding up of the Corporation, (ii) notified
      the Petitioner that they will not collaborate in the winding up of the
      Corporation, or (iii) notified the Petitioner that they will collaborate
      in the winding up of the Corporation but failed to do so at the
      satisfaction of the Petitioner, then the parties hereby irrevocably agree
      that upon application to the Trial Division of the Supreme Court of the
      Province of Nova Scotia, the Court shall render an order for winding up of
      the Corporation according to the rules set forth in Section 4.3 and in
      accordance with the Companies Winding Up Act (Nova Scotia).

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                                      -9-


4.5   SALE, MERGER AND ACQUISITION OF CONTROL

      In addition to the Exit Rights provided in Section 4.2 and following, a
      Shareholder may send at any time a Winding up Notice to the other
      Shareholder and the Corporation in the event of (i) the transfer or sale
      of all or substantially all of the asset of the other Shareholder, (ii)
      the merger of the other Shareholder with a third party; (except for
      mergers solely for the purpose of changing the legal domicile of a party)
      or (iii) the acquisition by a third party of the Control of the other
      Shareholder and the provisions of Sections 4.3 and 4.4 shall apply to any
      such Winding up Notice.

4.6   NO REGISTRATION

      Without prejudice to any other recourses that may be exercised in such a
      case, any Lien created, incurred, assumed or suffered to exist, directly
      or indirectly, in contravention of this Agreement, and any sale, transfer,
      assignment, alienation or other disposition of the Shares effected in
      contravention hereof (whether directly or indirectly) shall, for all
      intents and purposes, with regard to the other Shareholder and the
      Corporation, be null, void and without effect and shall not be registered
      in the books of the Corporation, any such registration being without
      effect

4.7   LEGEND OF SHARE CERTIFICATES

      All of the share certificates of the share capital of the Corporation
      shall bear the following conspicuous inscription:

            "Ownership, conveyance and encumbrance of the Shares represented by
            this certificate are subject to the terms of the Shareholders
            Agreement dated February 4, 2000."

4.8   DEFINITIONS

      All terms used in this Article 4 which are defined in the Collaboration
      Agreement, the IDI License and the Cepheid License are used herein with
      the meanings defined therein.




                                    ARTICLE 5

                                 CONFIDENTIALITY



5.1   UNDERTAKING

      The Shareholders hereby acknowledge and agree that they have been and will
      be given access to or otherwise come into contact with information
      relating to the businesses, operations, properties, assets, liabilities
      and financial conditions of the Corporation, of business partners of the
      Corporation, of a Shareholder or of a shareholder of a Shareholder,
      including without limitation, information relating to business plans and
      ideas, trade secrets, invention, processes, methods, know-how, policies,
      materials, results of operations, financial and statistical information,
      personnel data and customer, supplier and price lists, which are
      considered by

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      the Corporation, the business partner of the Corporation, the Shareholder
      or the shareholder of a Shareholder, as the case may be, to be valuable,
      secret and confidential (hereinafter referred to as the "Confidential
      Information"). Each of the Shareholders hereby agrees that it will not,
      for any purpose, at any time that it is a Shareholder and for a period of
      5 years following the date upon which it ceases to be a Shareholder, allow
      one of its shareholders, directors, officers, employees or agents during
      the same period, to make public, disclose, divulge, furnish, transfer,
      sell, release or otherwise make available to any Person, firm,
      association, partnership, syndicate, company or corporation any of the
      Confidential Information or otherwise use any of the Confidential
      Information or allow any of the Confidential Information to be used for
      any purpose other than, during the period during which a party hereto
      remains a Shareholder, for the purposes of advancing the interests of and
      for the entire benefit of the Corporation.

      The foregoing non-use and non-disclosure obligations assumed by each party
      shall not apply to information which (i) was in its possession prior to
      the date of execution of the Heads of Agreement, (ii) is disclosed to it
      by a third party not bound by obligations of confidentiality to the party
      disclosing the information or to any third party, or (iii) is generally
      available to the public.

5.2   SURVIVAL

      The undertaking set forth in Section 5.1 shall survive and continue in
      full force the winding up of the Corporation.




                                    ARTICLE 6

                                  MISCELLANEOUS



6.1   SUCCESSORS AND ASSIGNS

      The provisions of this Agreement shall, except as otherwise provided
      herein, enure to the benefit of and be binding upon the parties hereto and
      their respective representatives, successors assigns and each and every
      Person so bound shall make, execute and deliver all documents necessary to
      carry out this Agreement.

6.2   NOTICES

      Any notice or other communication to be given hereunder may be effectively
      given to a party by delivering the same at the addresses hereinafter set
      forth or by sending the same by prepaid registered mail, prepaid courier
      or telecopy or e-mail (in the case of telecopy or e-mail with confirmation
      of receipt) to such party at such addresses. Any notice so mailed shall be
      deemed to have been received on the third Business Day following the
      mailing thereof and if given by delivery or telecopy the same shall be
      deemed to have been received upon delivery or upon transmission. The
      mailing and telecopy address of the parties for the purpose hereof shall
      be:



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                                      -11-



      (a)   as to the Corporation:
            ---------------------

               Aridia Corp.
               2050 Rene-Levesque Blvd. West
               4th floor
               Sainte-Foy, Quebec
               G1V 2K8
               Attention: Dr. Pierre Coulombe
               Facsimile: (418) 681-5254

               And copy to: Thomas L. Gutshall
               Facsimile: (408) 541-4192

      (b)   as to IDI:
            ---------

               Infectio Diagnostic (I.D.I.) Inc.
               2050 Rene-Levesque Blvd. West
               4th floor
               Sainte-Foy, Quebec
               G1V 2K8
               Attention: Dr. Pierre Coulombe
               Facsimile: (418) 681-5254

      (c)   as to Cepheid:
            -------------

               Cepheid
               1190 Borregas Avenue
               Sunnyvale, CA, 94089-1302
               Attention: Thomas L. Gutshall
               Facsimile: (408) 541-4192


6.3   WAIVERS

      The rights and remedies of the Shareholders under this Agreement shall be
      cumulative and not exclusive of any rights or remedies which they would
      otherwise have and no failure or delay by any Shareholder in exercising
      any right shall operate as a waiver thereof, not shall any single or
      partial exercise of any power or right preclude its other or further
      exercise or the exercise of any other power or right.

6.4   AMENDMENTS

      This Agreement may be amended only by written agreement duly executed by
      all the parties hereto.

6.5   TIME OF ESSENCE

      Time shall be of the essence of this Agreement.



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6.6   COUNTERPARTS

      This Agreement may be executed in one or more counterparts each of which
      when so executed shall be deemed to be an original and such counterparts
      together shall constitute but one of the same instrument.

6.7   SEVERABILITY

      Any provision of this Agreement which is prohibited or unenforceable in
      any jurisdiction shall, as to such jurisdiction, be ineffective to the
      extent of such prohibition or unenforceability without invalidating the
      remaining provisions hereof in that jurisdiction or affecting the validity
      or unenforceability of such provision in any other jurisdiction.

6.8   REPLACEMENT OF HEADS OF AGREEMENT

      The present Agreement replaces and supersedes the Heads of Agreement and
      all other verbal or oral agreements, understandings and undertakings
      between the parties hereto relating to the transaction contemplated
      herein.

6.9   LANGUAGE

      The parties hereto have expressly required that this Agreement and all
      deeds, documents and notice relating thereto be drafted in the English
      Language. Les parties aux presentes ont expressement exige que la presente
      convention et tous les autres contrats, documents ou avis qui y sont
      afferents soient rediges en langue anglaise.

6.10  CONFLICT

      In the event of any conflict between the provisions of this Agreement on
      the one hand and the Memorandum and Articles of Association on the other,
      the provisions of this Agreement shall govern. Each Shareholder agrees to
      vote or cause to be voted the Shares owned by him as necessary so as to
      cause the Memorandum and Articles of Association to be amended to resolve
      any such conflict in favor of the provisions of this Agreement.


      IN WITNESS WHEREOF this Agreement has been executed on the date
hereinabove first set forth.


INFECTIO DIAGNOSTIC (I.D.I.) INC.            ARIDIA CORP.


Per: /s/ DR. PIERRE COULOMBE                 Per: /s/ DR. PIERRE COULOMBE
    ----------------------------                 -----------------------------
      Dr. Pierre Coulombe                          Dr. Pierre Coulombe

CEPHEID
                                             Per: /s/ THOMAS L. GUTSHALL
                                                 -----------------------------
                                                     Thomas L. Gutshall
Per:   /s/ THOMAS L. GUTSHALL
    ------------------------------
        Thomas L. Gutshall