Monday, 24 March 2014

Understanding the host-virus interaction in chronic HTLV-I infection with the help of mathematical modelling

In this post Aaron Lim, a DPhil student at the WCMB and the EEID, discusses his work on within-host mathematical modelling of host-virus interactions.


I am interested in building a better understanding of the host-virus dynamics of chronic viral infections, specifically in the context of human T-cell lymphotropic virus type I (HTLV-I), which is in fact the first discovered human retrovirus, identified independently by researchers in both Japan and the United States in the late 1970's to early 1980's. I was introduced to this topic during my M. Sc. programme at the University of Alberta in Canada, under the supervision of Prof Michael Li, and was fascinated by the observation that, despite three decades of HTLV-I research, there still remained many unanswered questions about the mechanisms of viral persistence and immunopathology. After completing my M. Sc., I decided to continue my research by pursuing a DPhil here at Oxford, where I am jointly supervised by Prof Philip Maini in the Wolfson Centre for Mathematical Biology (WCMB), and Prof Sunetra Gupta in the Evolutionary Ecology of Infectious Disease (EEID) group at the Department of Zoology. It is my belief that mathematical modelling, alongside experimental advances, can help us break apart the complex mechanisms of the host-virus interaction and identify the key underlying principles of persistent infection in the presence of host immunity. In this post, I will discuss a within-host model of HTLV-I that we have developed which forms the foundation of my DPhil project.

Background and Motivation

Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterised by life-long infection and risk of developing one of two major, clinically independent diseases: adult T-cell leukaemia/lymphoma (ATL), an aggressive blood cancer, and HAM/TSP, a progressive neurological and inflammatory disease. The virus primarily infects CD4+ helper T-cells, a subset of lymphocytes whose principal role is to enhance the function of adaptive immunity, for example, by secreting pro-inflammatory cytokines, facilitating antigen presentation, and triggering the activation of other types of immune cells. Infected individuals typically mount a large, chronically activated CD8+ cytotoxic T-lymphocyte (CTL), or so-called 'killer T-cell', response against HTLV-I-infected cells, but ultimately fail to effectively eliminate the virus. Moreover, identification of determinants to disease manifestation has thus far been elusive.

How the virus is able to evade host immunity and avoid viral clearance is a key issue in current HTLV-I research. Understanding the complex mechanisms of HTLV-I persistence is a crucial step to developing effective ways to disrupt the virus life-cycle and may help identify promising new treatment strategies to reduce the severity of HTLV-I infection and associated disease. Therefore, we focus our efforts on elucidating this issue.


Asquith and Bangham (2008) have recently proposed an experimental hypothesis for the persistence of HTLV-I in vivo which motivated the formulation of a mathematical model by Li and Lim (2011) that illustrates the balance between latency and activation in the target cell dynamics of the viral infection (this was work done during my M. Sc.). In the first part of my DPhil, I have extended this previous model by incorporating the role of a constantly changing anti-viral immune environment mediated by CTLs. The resulting model, which I term the 'baseline model', is a four-dimensional system of ordinary differential equations that describes the dynamic interactions among viral expression, infected target cell activation, and the HTLV-I-specific CTL response. A schematic picture of the baseline model is shown below:

A schematic representation of the biological mechanism of HTLV-I infection in vivo that motivates the formulation of the baseline model. Figure reproduced (with slight modifications) from Lim and Maini (2014).
To fully understand the dynamics of our baseline model, we have made use of standard mathematical techniques including non-dimensionalisation, stability, asymptotic, and bifurcation analyses to investigate the system. We have identified a sharp threshold parameter, the basic reproduction number for viral infection R0, which completely characterises the global behaviour of solutions to the model: if R0 < 1, the infection is cleared; if R0 > 1, the infection is chronic. The global stability of the respective equilibria in each of the two cases for R0 has been shown by constructing appropriate Lyapunov functions.

After having established the global dynamics of the model, we asked biologically relevant questions relating to HTLV-I persistence and used the model to try and address these issues. In particular, we explored the roles of certain key parameters on the outcome of the infection dynamics using bifurcation analysis and computational methods. We focussed on three issues: (i) Why is HTLV-I not silent? In other words, what benefit does the HTLV-I provirus gain in becoming activated and expressing viral antigens? (ii) What role do CTLs play in the outcome of infection? (iii) Do our results give insights to the development of HTLV-I-associated disease?

Main Biological Conclusions

Our baseline mathematical model of HTLV-I infection offers important insights to the evolution of viral persistence. A few main results arising from the model are the following.

  • Infected target cell activation and expression of viral antigens is required for the establishment of HTLV-I infection and aids viral persistence.
  • The HTLV-I-specific CTL response determines proviral load despite frequent viral latency, yet is unable to completely eliminate the virus due to the small proportion of activated proviral cells that are aggressively propagating the infection. Moreover, efficient control of viraemia is dependent on a high rate of CTL-mediated lysis and not on the frequency of HTLV-I-specific immune effectors.
  • The extent of proviral activation rather than the size of the proviral load may distinguish clinical status and suggests a route for disease.

Outlook and the Road Ahead

The purpose of the baseline model was to develop a consistent theoretical framework that can help shed light on specific, biologically relevant questions that are of interest to experimentalists and theoretical immunologists trying to understand the complicated host-pathogen dynamics of chronic viral infections such as HTLV-I. However, we have only just scratched the surface; there are still many interesting aspects of the host-virus interaction that require deeper exploration. It is with hope that, with the rise of interdisciplinary collaborations, we can use each of our respective tools and areas of expertise to work together and build a clearer picture of all these issues.


B. Asquith and C. R. M. Bangham (2008). How does HTLV-I persist despite a strong cell-mediated response?, Trends in Immunol., 29:4--11.

M. Y. Li and A. G. Lim (2011). Modelling the Role of Tax Expression in HTLV-I Persistence in vivo. Bull. Math. Biol., 73:3008-29.

A. G. Lim and P. K. Maini (2014). HTLV-I infection: A dynamic struggle between viral persistence and host immunity. J. Theor. Biol.,


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