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Stochastic processes in Health & Disease

PGR-P-259

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
Dr Martin Lopez Garcia
Schools
School of Mathematics
Research groups/institutes
Applied Mathematics
<h2 class="heading hide-accessible">Summary</h2>

During the last years, increasing efforts are being devoted to better understanding a wide range of processes arising in Health &amp; Disease. In particular, mathematical modelling of infectious diseases is a research area which has been increasingly growing during the last years. When analysing a process in Health &amp; Disease, both deterministic and stochastic approaches can be implemented. Deterministic approaches imply that, when analysing a, for example, Biological system, identical initial conditions would always lead to the same future dynamics of the corresponding process. On the other hand, stochastic approaches are used to incorporate randomness when modelling these processes, so that two observations of the same process with identical initial conditions can still lead to different future dynamics or final outputs. Stochastic approaches are usually more appropriate when analysing the spread of a disease among individuals in a small or highly heterogeneous population, when considering Biological processes where extinction events play an important role, or for modelling processes which are intrinsically and naturally random. The stochastic modelling of processes in Health &amp; Disease usually leads to the analysis of continuous-time Markov chains, where one of the main assumptions is that events occur in these processes after Exponentially distributed random times. This hypothesis, which can be too strict when studying some particular systems, allows one to analyse these processes both from a mathematical and computational perspective. The development and spread of infectious diseases is a combination of processes occurring at different scales: from the genetic and cellular, to the host and population levels; see, for example, the research paper [1], where our research group at Leeds focuses on analysing, at the cellular level, molecular processes involved in the immune response against infections, research paper [2] where we analyse processes at the within-host level related to the dynamics of cell populations which form part of our immune system during non-infection periods, or research paper [3] where we analyse the spread of an epidemic among a small group of highly heterogeneous individuals. This project will involve the development of new and use of existing both analytical and computational approaches, and will thus include a significant amount of programming. The candidate should also be willing to participate in inter-disciplinary collaborations potentially arising during the project.

<h2 class="heading hide-accessible">Full description</h2>

<p>For more information about this project, the&nbsp;<a href="http://www1.maths.leeds.ac.uk/school/research/mathbiomed/">research activity of our group</a>, and&nbsp;<a href="https://matml.github.io/">recent publications</a>&nbsp;by Dr Mart&iacute;n L&oacute;pez-Garc&iacute;a.</p> <p>References:&nbsp;</p> <ol> <li>de la Higuera L, L&oacute;pez-Garc&iacute;a M, Lythe G, Molina-Par&iacute;s C (2017) IL-2 stimulation of regulatory T cells: a stochastic and algorithmic approach. In: Pahle J, Matth&auml;us F, Graw F (eds.) Modeling Cellular Systems, 81-105.</li> <li>Artalejo JR, G&oacute;mez-Corral A, L&oacute;pez-Garc&iacute;a M, Molina-Par&iacute;s C (2017) Stochastic descriptors to study the fate and potential of naive T cell clonotypes in the periphery. Journal of Mathematical Biology. 74: 673-708.</li> <li>L&oacute;pez-Garc&iacute;a M (2016) Stochastic descriptors in an SIR epidemic model for heterogeneous individuals in small networks. Mathematical Biosciences 271: 42-61.</li> <li>Kulkarni VG (1995) Modeling and analysis of stochastic systems. Boca Raton, CRC Press.</li> <li>Allen LJS (2010) An introduction to stochastic processes with applications to biology. New Jersey, CRC Press.</li> <li>He QM (2014) Fundamentals of matrix-analytic methods. New York, Springer.</li> </ol> <p>The earliest start date for this project is 1 October 2020.&nbsp;</p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Stochastic processes in Health &amp; Disease&rsquo; as well as&nbsp;<a href="https://physicalsciences.leeds.ac.uk/staff/54/dr-martin-lopez-garcia">Dr Mart&iacute;n L&oacute;pez-Garc&iacute;a</a>&nbsp;as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funding Students</strong></p> <p><strong>Funding Eligibility</strong></p> <p><strong>UK/EU</strong> &ndash;&nbsp;Leeds Doctoral Scholarship Award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years, School of Mathematics Scholarship award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p> <p><strong>International Students</strong> &ndash;&nbsp;China Scholarship Council-University of Leeds Scholarship Award paying Academic Fees for 3 years,&nbsp;School of Mathematics Scholarship award paying Academic Fees for 3 years, Commonwealth Scholarship and Commonwealth Split Site Scholarships.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p>

<h2 class="heading">Contact details</h2>

<p>For further information regarding your application, please contact Doctoral College Admissions by&nbsp;email:&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>, or by telephone: +44 (0)113 343 5057.</p> <p>For further information regarding the project, please contact Dr Martin Lopez-Garcia by email:&nbsp;&nbsp;<a href="mailto:M.LopezGarcia@leeds.ac.uk">M.LopezGarcia@leeds.ac.uk</a></p>


<h3 class="heading heading--sm">Linked funding opportunities</h3>
<h3 class="heading heading--sm">Linked research areas</h3>