Mathematical models for preclinical drug trials: small molecule drugs and antibody drug conjugates

This multidisciplinary and collaborative PhD will use advanced mathematical modelling to design optimal drug treatments for cancer.

Start date

1 January 2023


3 years initially

Application deadline

Funding source

University of Surrey

Funding information

The Department of Mathematics has a number of fully funded PhD studentships for UK nationals. These studentships will include the tuition fees and a tax-free stipend. The Department has also a few scholarships for partial and full funding for overseas fees for exceptional applicants. However, funding for overseas students is limited and applicants are encouraged to find suitable funding themselves.


Preclinical evaluation of drug efficacy plays a fundamental role in the development of cancer treatments, with the aim being to evaluate drug action and anti-tumour effect. Fundamental to these preclinical studies is the use of mathematical models to describe the tumour dynamics and evaluate the anti-tumour effect. Typically, these models take the form of simple growth laws based on empirical descriptions of the data combined with larger systems of equations describing the drug action. As more varied data is incorporated into the pharmaceutical trial pipeline the challenge arises to develop mechanistic models that can account for this additional complexity while still being fit-for-purpose in an industrial context.

The proposed project builds on the currently ongoing research collaboration of Dr Dunlop and Prof Derks at the University of Surrey with Dr James Yates (Scientific Director, PKPD at GSK). Out of this collaboration a mechanistic model has been developed based on a spatially resolved model for tissue growth. This model, which develops mechanistic descriptions of drug and nutrient diffusion in the tumour, has been developed for small molecule drugs. We plan to develop this model further exploring its use in designing optimal dosing protocols and incorporating pharmacokinetic/pharmacodynamic descriptions of drug action. A key focus are new treatments, including antibody drug conjugates, for which spatially resolved modelling is particularly important. Ultimately the aim is to improve drug translation from pre-clinical to clinical studies.

The project will require the ability to work collaboratively and across discipline boundaries. As well as requiring advanced modelling skills, the PhD will require facility with both partial differential equations, nutrient diffusion and dynamical systems modelling. Importantly models will be tested and validated against current best practice and pre-clinical data so the student will need a willingness to engage with real-world data and data fitting.

Eligibility criteria

Applicants should have a minimum of a first class honours degree in mathematics, the physical sciences or engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, though exceptional BSc students will be considered.

English language requirements 

IELTS minimum 6.5 overall, with 6.0 in writing, or equivalent.

How to apply

Applications should be submitted via the Mathematics PhD Research programme page on the "Apply" tab. Please clearly state the studentship title and supervisor on your application.

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Application deadline

Contact details

Cesare Tronci



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