<PAGE>   1
                                                                   EXHIBIT 10.34

                 [TRUST COMPANY OF THE SOUTH LETTERHEAD]

October 13, 1998

Mr. Joseph M. Cummins, DVM, PhD
President and Chief Executive Officer
Amarillo Biosciences, Inc.
800 West Ninth Avenue
Amarillo TX 79101-3206

Re: Engagement

Dear Dr. Cummins:

This letter is to confirm our understanding that Amarillo Biosciences, Inc. (the
"Company") has engaged Trust Company of the South ("TCOS") to act as its
Executive Advisor.

TCOS's services in connection with this engagement will include assisting the
Company, in (1) Preparation of a corporate profile suitable for use with brokers
and investors (research, write, design, print and distribute). All content is
subject to the Company's approval, (2) Designing and implementation of a plan
for both the short and long term promotion of investor interest in the Company,
(3) Interfacing with the investment community on behalf of the Company and
publicly promoting investor interest in the Company, (4) Preparation of press
releases, upon request, and introduction of the Company to appropriate financial
writers and media persons, (5) Enlistment of additional market makers for the
Company's stock, (6) Development of a list of key brokers that can be cultivated
on behalf of the Company and its stock, and seek to enhance the interest of
these brokers in the Company, (7) Assistance, when requested, in the preparation
of presentations to broker and investor groups, (8) Development, with Company's
officers of an ongoing in-house program for investor relations, (9) Coordination
with management and other board members in the selection of additional outside
board members, (10) Evaluation of the benefits of listing the Company's
securities on the American Stock Exchange when and if appropriate, (11)
Evaluation and recommendations regarding utilizing personal and corporate trust
services provided by TCOS.

The Company agrees to promptly reimburse TCOS for all expenses incurred by TCOS
pursuant to this engagement. Such expenses shall include but not be limited to,
transportation, lodging, mileage, meals, parking, tips, copying, printing,
telephone, overnight delivery, computer research, postage, telecopy and other
miscellaneous items. The Company shall have the right to pre-approve expense
charges which would exceed $7,500.00 in one calendar month.

The term of this Engagement will be for a period of five years from the
effective date of this letter agreement provided, however, that the Company may
terminate the Engagement prior to the expiration of said term by giving written
notice of termination to TCOS at least ten days prior to any six months
anniversary of this letter agreement.

Notwithstanding the termination of this agreement, the expense reimbursement
provisions contained herein, the indemnification and contribution provisions set
forth on Schedule I attached hereto and incorporated herein, and the
Non-Disclosure Agreement set forth on Schedule II and incorporated herein shall
survive and will remain in full force and effect.



<PAGE>   2

Mr. Joseph M. Cummins, DVM, PhD.
Amarillo Biosciences, Inc.
Engagement
October 13, 1998
Page 2

As remuneration for the aforementioned services, the Company agrees to
pay TCOS a fee of $6,000 per month. Additionally, TCOS is to receive a
Warrant to purchase up to 112,000 shares of the Company's common
stock at a price of $1.75 per share.

If, at any time from the date hereof through September 29, 2003, the Company
proposes to register its securities under the Securities Act of 1933 ("the Act")
or any such securities of the Company held by its stockholders (in any such
case, other than in connection with a merger, acquisition or pursuant to Form
S-8 or successor form), it will give written notice of its intention to do so by
registered mail ("Notice"), at least thirty (30 business days prior to the
filing of each such registration statement), to the Warrant Holder. Upon the
written request of the Warrant Holder, made within fifteen (15) business days
after receipt of the Notice, that the Company include any of the Warrant
Holder's shares of common stock of the Company in the proposed registration
statement (such request to specify the number of shares to be so included), the
Company shall use its best efforts to effect the registration under the Act of
the securities which it has been so requested to register, at the Company's sole
cost and expense and at no cost or expense to the Warrant Holder. Nothing herein
contained shall prohibit the Company from granting so-called "piggyback" rights
superior to or equal to the rights granted herein to any person or entity not
affiliated with the Company. Notwithstanding the provisions of this paragraph,
the Company shall have the right at any time after it shall have given Notice
(irrespective of whether any written request for inclusion of such securities
shall have already been made) to elect not to file any such proposed
registration statement, or to withdraw the same after the filing but prior to
the effective date thereof. The Warrant will be exercisable beginning on the
effective date of this letter agreement and will expire if not exercised the
later of: (i) five years from the effective date of this letter agreement, or
(ii) eight years from the effective date of this letter agreement if the
holder(s) of the Warrant has not been afforded the opportunity to register the
underlying securities in a public offering of the Company's securities during
the initial five year period. The expense of registration will be paid by the
Company. In accordance with applicable securities laws, the Warrant will be
transferable at the written instruction of TCOS. The Warrant and underlying
common shares are subject to adjustment, proratably, in price and number in the
case of certain transactions such as mergers, recapitalization, stock splits and
stock dividends. The Warrant holder will have the right of co-sale. The Warrant
holder will also have "cheap stock" dilution protection, so that such holder
receives the right to additional shares and/or a lesser share price in the event
shares are issued at a below market price. The Company and TCOS shall undertake
to have a formal Warrant Agreement finalized on or before October 31, 1998 and
both parties understand the aforementioned is only a brief summary of certain
material provisions of the Warrant.

In connection with TCOS's services, the Company will furnish or cause
to be furnished to TCOS such information and data (hereinafter
referred to as the "Information") relating to the Company and such
access to the Company's officers, directors and employees and
independent contractors, as TCOS reasonably deems necessary or as TCOS
reasonably requests. The Company will be solely responsible for the
contents of any and all written or oral communications provided. The
Company represents and warrants that any such communications and all
information including, but not limited to, financial information, will
not contain any untrue statements of a material fact or omit to state a
material fact necessary in order to make the statements therein not
misleading in light of the circumstance under which such statements are
or will be made. The Company recognizes and confirms that in TCOS's
performance of its services hereunder, (a) TCOS may rely upon the
accuracy and completeness of the information without independent
verification and (b) TCOS does not assume responsibility for the
accuracy or completeness thereof whether or not it makes an independent
verification. TCOS shall provide the Company for its review, comment
and




<PAGE>   3

Mr. Joseph M. Cummins, DVM, PhD.
Amarillo Biosciences, Inc.
Engagement
October 13, 1998
Page 3

approval copies of any tangible communications whether written or
recorded on audio, video or film media, which TCOS may give to any
person in providing services under this Engagement. TCOS shall provide
such copies to the Company a minimum of three business days prior to
TCOS's first proposed use of such materials.

Any information obtained by TCOS pursuant to the Engagement shall be
governed by a Non-Disclosure Agreement between TCOS and the Company in
the form attached hereto as Schedule 11.

TCOS shall retain the legal status of an independent contractor. In no
event shall TCOS be or be deemed to be an employee or agent of the
Company, or to qualify for benefits afforded such persons as Company
employees. TCOS has no power to act for, represent or bind the Company.

The Company hereby irrevocably agrees to provide the indemnification as
set forth in Schedule I to TCOS and other parties specified therein.

This letter agreement shall be governed by, and construed in accordance
with, the laws of the State of South Carolina without regard to
principles of conflict of laws.

This letter agreement has been and is made solely for the benefit of
the Company and TCOS and its agents, employees, officers, directors,
stockholders and controlling persons and their respective successor and
assigns and heirs, and no other person shall acquire or have any right
under or by virtue of this letter agreement.

Please confirm that the foregoing accurately reflects our understanding
by signing, dating and returning to us the attached copy of this letter
agreement, along with your check for $8,500 representing the initial
monthly fee and an expense advance of $2,500, whereupon when accepted
and approved by the TCOS's Trust Committee this will become a binding
and effective agreement between us.

                                                      Very truly yours,

                                                      TRUST COMPANY OF THE SOUTH

                                                      /s/ ANDY M. CRANE, SR.
                                                      --------------------------
                                                       Andy M. Crane
                                                       President & CEO

Agreed and Accepted
AMARILLO BIOSCIENCES, INC.


By:  /s/ JOSEPH M. CUMMINS
  ------------------------------------
   Joseph M. Cummins, DVM, PhD.
   President & Chief Executive Officer


Date: 15th October, 1998
     ---------------------------------


AMC:ctjk
Enclosures
<PAGE>   4





                                    SCHEDULE I
                   TO ENGAGEMENT LETTER DATED OCTOBER 13,1998
                       BETWEEN TRUST COMPANY OF THE SOUTH
                         AND AMARILLO BIOSCIENCES, INC.

         a) The Company agrees to indemnify and hold TCOS, its affiliates and
any affiliated entities of TCOS and their respective officers, directors,
partners, employees, agents and controlling persons within the meaning of
Section 15 of the Securities Act of 1933 or Section 20 of the Securities
Exchange Act of 1934 (TCOS and each such entity and person being hereinafter
called an "Indemnified Person") harmless from and against any and all claims,
liabilities, losses, damages, costs and expenses incurred (including fees and
disbursements of counsel) by them which are (A) caused by, related to or arise
out of (i) actions taken or omitted to be taken (including any untrue statements
made or any statements omitted to be made) by the Company or (ii) actions taken
or omitted to be taken (including any untrue statements omitted to be made) by
an Indemnified Person with the Company's consent or in conformity with actions
taken or omitted to be taken by the Company pursuant to the accompanying letter
(B) otherwise related to or "arising out of TCOS's activities performed pursuant
to the accompanying letter agreement (including, without limitation, its role as
Executive Advisor and agent), the services contemplated by the accompanying
letter agreement or TCOS's role in connection therewith. The Company will not,
however, be responsible for any such claims, liabilities, losses, damages, costs
or expenses pursuant to clause (B) of the preceding sentence which have been
finally determined by a court of competent jurisdiction to have primarily and
directly resulted from willful misconduct or negligence on the part of the
Indemnified Person seeking indemnification hereunder.

         b) Notwithstanding anything expressed or implied herein to the
contrary, the indemnity provided for herein shall cover the amount of any
settlements entered into by an Indemnified Person in connection with any claim
for which an Indemnified Person may be indemnified hereunder; provided,
however, that an Indemnified Person shall not enter into any such settlement
unless the Company has consented thereto (which consent shall not be
unreasonably withheld). No settlement binding on an Indemnified Person may be
made without the consent of such Indemnified Person (which consent shall not be
unreasonably withheld).

         c) The Company and TCOS agree that if any indemnification sought by an
Indemnified person pursuant to this paragraph is held by a court to be
unavailable for any reason other than that specified in the second sentence of
paragraph (a) above, then (whether or not TCOS is the Indemnified Person), in
order to provide just and equitable contribution, the Company and TCOS shall
contribute to the claims, liabilities, losses, damages, costs and expenses for
which such indemnification is held unavailable in such proportion as is
appropriate to reflect the relative benefits of the Company, on the one hand,
and TCOS on the other hand, in connection with the services or services
contemplated by the accompanying letter agreement, and also relative fault of
the Company, on the one hand, and TCOS on the other hand, in connection with the
services or services contemplated by the accompanying letter agreement, and also
relative fault of the Company, on the one hand, and TCOS, on the other hand,
subject to the limitation that in any




<PAGE>   5




                                    SCHEDULE I
                   TO ENGAGEMENT LETTER DATES OCTOBER 13,1998
                        BETWEEN TRUST COMPANY OF THE SOUTH
                         AND AMARILLO BIOSCIENCES, INC.
                                    PAGE TWO.

event TCOS's aggregate contribution to all claims, liabilities, losses, damages,
costs and expenses with respect to which contribution is available hereunder
shall not exceed the amount of fees (but not expenses) actually received by TCOS
pursuant to the accompanying letter agreement. No person found liable for a
fraudulent misrepresentation shall be entitled to contribution from any person
who is not also found liable for such fraudulent misrepresentation.

You also agree that no Indemnified Person shall have any liability (whether
direct or indirect in contract or tort or otherwise) to the Company for or in
connection with the accompanying letter agreement, the services contemplated
hereby or TCOS's role in connection therewith, except for any such liability for
losses, claims, damages, liabilities or expenses incurred by the Company that
are determined by final judgment or a court of competent jurisdiction to have
resulted directly from willful misconduct or negligence of such Indemnified
Person.

The provisions in this is Schedule I shall remain operative and in full force
and effect regardless of the termination or expiration of the Engagement
pursuant to the accompanying letter agreement.

<PAGE>   6



                                   SCHEDULE II
                            NON-DISCLOSURE AGREEMENT
                   TO ENGAGEMENT LETTER DATED OCTOBER 13,1998
                       BETWEEN TRUST COMPANY OF THE SOUTH
                         AND AMARILLO BIOSCIENCES, INC.

                                    RECITALS

         The parties are exploring areas of common business interest. In the
course of these discussion, the parties have delivered or will deliver to each
other certain information which the parties desire to remain confidential,
including descriptive memoranda, appraisals, financial statements or summaries,
correspondence records or other specific financial, technical, commercial or
other information regarding their businesses and affairs, whether or not such
material is specifically marked or designated as confidential (the "Confidential
Information"). The parties desire to assure each other that all Confidential
Information exchanged will be treated with utmost confidence and will not be
used by either party to the detriment of the other. The party who receives
Confidential Information in any instance is referred to as "Recipient" and the
part who discloses Confidential Information is referred to as "Discloser".

                                   AGREEMENTS

         In consideration of the recitals and the mutual agreements which
follow, the parties agree:

         1. Any Confidential Information exchanged is provided only for the
purposes of assisting each party in exploring their common interests. Recipient
acknowledges that Confidential Information is proprietary and confidential and
that Discloser would suffer great loss and irreparable harm if Recipient, its
affiliates, agents or employees would improperly use the Confidential
Information or disclose it to Discloser's customers, employees, competitors,
potential competitors or other parties. Recipient agrees to use Confidential
Information solely for the purpose of evaluating the parties' common interests
and to prevent the use of Confidential Information for any commercial purpose.

         2. Recipient acknowledges that the restrictions of this Agreement are
reasonable and the consideration provided is sufficient to fully and adequately
compensate Recipient for agreeing to these restrictions. Recipient shall not
improperly use or disclose to others or permit the improper use or disclosure of
any of the Confidential Information or any analysis, modifications or
improvements derived from Confidential Information. Recipient shall protect
Confidential Information by using the same degree of care, but no less than a
reasonable degree of care, to prevent the unauthorized use, dissemination or
publication of the Confidential Information as Recipient uses to protect its own
confidential information of a like nature.



<PAGE>   7


                                   SCHEDULE II
                            NON-DISCLOSURE AGREEMENT
                   TO ENGAGEMENT LETTER DATED OCTOBER 13,1998
                       BETWEEN TRUST COMPANY OF THE SOUTH
                         AND AMARILLO BIOSCIENCES, INC.
                                    PAGE TWO.

         3. Recipient agrees upon written request of Discloser, to return all
materials containing Confidential Information, including all existing copies,
extracts, photographs and summaries thereof, within two business days of such
request.

         4. Nothing contained herein shall be construed as restricting or
creating any liability for the disclosure, communication or use of the following
types of information:

            (a) information which, at the time of disclosure hereunder, was
published or know publicly or was otherwise in the public domain:

            (b) information which after disclosure hereunder, is published or
becomes publicly know or otherwise in the public domain other than as a result
of a breach of this Agreement, or

            (c) information which was disclosed to the recipient in good faith 
by a third part who was not, and is not, under any obligation of confidence or
secrecy to the other party hereto at the time of such disclosure.

         5. Recipient shall be responsible to Discloser for any breach of the
provisions of this agreement by persons who are within Recipient's reasonable
control. Recipient shall be entitled to an injunction or injunctions to prevent
breaches of any provisions of this Agreement and may specifically enforce such
provisions in any action instituted in any court having appropriate
jurisdiction. Recipient agrees to indemnify and hold Discloser harmless from and
against all loss, damage, cost or expense (including reasonable attorneys' fees)
resulting from or arising out of any breach of this Agreement by Recipient.
These specific remedies are in addition to any other remedy to which Discloser
may be entitled at law or in equity. Nothing contained in this Agreement shall
be deemed to prevent the disclosure of any Confidential Information if such
disclosure is legally required, in the opinion of counsel to Recipient, to be
made in a judicial, administrative or governmental proceeding to disclose any
Confidential Information and to allow Discloser a reasonable time to oppose such
process.

         6. Recipient shall not be permitted to disregard its obligations under
this Agreement by using Confidential Information to guide a search of
publications or other publicly available materials or be selecting a series of
items of knowledge from unconnected sources in the public domain and fitting
them together through use of Confidential Information.

         7. Without the other party's consent, neither party nor its principals,
agents, employees or representatives, will disclose to any person the fact that
discussions or negotiations are taking



<PAGE>   8



                                   SCHEDULE II
                            NON-DISCLOSURE AGREEMENT
                   TO ENGAGEMENT LETTER DATED OCTOBER 13, 1998
                       BETWEEN TRUST COMPANY OF THE SOUTH
                         AND AMARILLO BIOSCIENCES, INC.
                                   PAGE THREE.

place unless required by law; provided, however, each party will consult
concerning the content of any such disclosure with the other prior to making the
disclosure.

         8.  Neither party acquires any intellectual property rights under this
Agreement except the limited right to use the Confidential Information for the
purpose described in section 1.

         9.  Except for the terms of this Agreement, none of the parties shall 
be committed in any way with respect to the matters discussed by them, unless
and until a definitive agreement with respect thereto is executed.

         10. This Agreement is the parties' complete understanding with respect
to the subject matter hereof and may only be amended in writing signed by both
parties. The parties' respective obligations shall survive the execution of this
Agreement. This Agreement may not be assigned in whole or in part. The
provisions of this Agreement shall be governed by and construed in accordance
with the laws of the State of South Carolina.