Mathematical modelling and investigation of oncolytic therapies for cancer
: The role of macrophages in tumour-virus interactions

  • Nada Almuallem

Student thesis: Doctoral ThesisDoctor of Philosophy


There is much evidence in the literature supporting the hypothesis that replicating oncolytic viruses provide promising treatment strategies against cancer. However, the success of these viral therapies depends mainly on the complex interactions between the virus particles and the host immune cells in tumour-microenvironment. Among these immune cells, macrophages represent one of the first line of defence against viral infections.

In this thesis, we start with a simple model that describes the interactions between a commonly-used oncolytic virus, the Vesicular Stomatitis Virus (VSV), and two extreme types of macrophages: the pro-inflammatory M1 cells (which seem to resist infection with VSV) and the anti-inflammatory M2 cells (which can be infected with VSV) [152]. We investigate the long-term behaviour of the model by focusing on steady states and limit cycles, and study changes in this long-term dynamics as we vary different model parameters. The proliferation and decay rates of macrophages play an important role on the existence and stability of steady states where the virus is present. Moreover, through local and global sensitivity analysis we show that the parameters that have the highest impact on the level of virus particles in the system are the viral burst size (from infected macrophages), the virus infection rate, and the virus elimination rate.

The second investigation presents a mathematical model to illustrate the dynamics between breast cancer tumour cells, an oncolytic virus (VSV), and tumour-infiltrating macrophages with different phenotypes which can impact the dynamics of oncolytic viruses. We use this model to propose new biological hypotheses regarding the impact on tumour elimination/relapse/persistence of: (i) different macrophage polarisation/re-polarisation rates; (ii) different infection rates of macrophages and tumour cells with the oncolytic virus; (iii) different viral burst sizes for macrophages and tumour cells. We show that increasing the rate at which the oncolytic virus infects the tumour cells can delay tumour relapse and even eliminate tumour. Increasing the rate at which the oncolytic virus particles infect the macrophages can trigger transitions between steady state dynamics and oscillatory dynamics, but it does not lead to tumour elimination unless the tumour infection rate is also very large. Moreover, we confirm numerically that a large tumour-induced M1/M2 polarisation leads to fast tumour growth and fast relapse (if the tumour was reduced before by a strong anti-tumour immune and viral
response). The increase in viral-induced M2/M1 re-polarisation reduces temporarily the tumour size, but does not lead to tumour elimination. Finally, we show numerically that the tumour size is more sensitive to the production of viruses by the infected macrophages.

The third investigation involves a delay in viral production from infected M2 macrophages in two separated models; the first model is with the absence of tumour, while the second model the tumour has been considered. We use these two models to propose new biological hypotheses regarding the impact on viral load and tumour elimination/control of: (i) the effect of delaying the VSV production from infected macrophages; (ii) the importance of the latently infected macrophages. We investigate both models in two cases where the death rates of M1 and M2 macrophages are equal or different. In the absence of the tumour, the case where the death rates are equal demonstrates that increasing the delay induces decreasing in virus levels, while the case where the death rates are not equal, leads to an increase in the virus levels. In the presence of the tumour, the case where the death rates are equal also leads to a decrease in the virus levels. However, the case when the death rates are different can lead to either a decrease in these virus levels, if the latently infected M2 cells don’t impact the persistence of viruses and tumour cells; or to a slight increase in these virus levels when latently infected M2 cells impact their persistence. Finally, we show the relation between the delay in the release of viral particles and the role of latently infected macrophages on the elimination/persistence of tumour states.

In our final investigation, we develop a PDE model for the spatial interaction between a virus-macrophages-tumour interaction. We investigate numerically the impact of random movement of macrophages and virus particles on tumour spread. We calculate analytically the speed at which the tumour invades the domain (in a travelling wave manner).
Date of Award2021
Original languageEnglish
SupervisorRaluca Eftimie (Supervisor) & Dumitru Trucu (Supervisor)


  • Cancer modelling
  • oncolytic viruses
  • macrophages

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