Research Article: Investigating Macrophages Plasticity Following Tumour–Immune Interactions During Oncolytic Therapies

Date Published: August 13, 2019

Publisher: Springer Netherlands

Author(s): R. Eftimie, G. Eftimie.

http://doi.org/10.1007/s10441-019-09357-9

Abstract

Over the last few years, oncolytic virus therapy has been recognised as a promising approach in cancer treatment, due to the potential of these viruses to induce systemic anti-tumour immunity and selectively killing tumour cells. However, the effectiveness of these viruses depends significantly on their interactions with the host immune responses, both innate (e.g., macrophages, which accumulate in high numbers inside solid tumours) and adaptive (e.g., documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells). In this article, we consider a mathematical approach to investigate the possible outcomes of the complex interactions between two extreme types of macrophages (M1 and M2 cells), effector documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells and an oncolytic Vesicular Stomatitis Virus (VSV), on the growth/elimination of B16F10 melanoma. We discuss, in terms of VSV, documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ and macrophages levels, two different types of immune responses which could ensure tumour control and eventual elimination. We show that both innate and adaptive anti-tumour immune responses, as well as the oncolytic virus, could be very important in delaying tumour relapse and eventually eliminating the tumour. Overall this study supports the use mathematical modelling to increase our understanding of the complex immune interaction following oncolytic virotherapies. However, the complexity of the model combined with a lack of sufficient data for model parametrisation has an impact on the possibility of making quantitative predictions.

Partial Text

The increase in the incidence of skin cancers, combined with the advances in understanding the molecular biological mechanisms involved in tumour progression and interactions between melanoma cells and immune cells, has led to the development of several immune strategies for the treatment of these cancers (Dharmadhikari et al. 2015). Among these strategies, the use of oncolytic virotherapies is emerging as an important approach in cancer treatment, due to their potential of inducing systemic anti-tumour immunity in addition to selectively killing cancer cells (Kaufman et al. 2016; Fukuhara et al. 2016; Filley and Dey 2017). In spite of current expectations that oncolytic virus therapy will become in the future a standard therapy option for all cancer patients (Fukuhara et al. 2016), there are still limitations of this therapy. The reduced effectiveness of the oncolytic viruses injected into cancer patients depends not only on the pathogenic nature of virally encoded genes, but also on the interactions between the virus and the host innate and adaptive immune responses (Melcher et al. 2011; Kaufman et al. 2016; Fukuhara et al. 2016; Filley and Dey 2017).

To investigate the effect of M1 and M2 macrophages on the anti-tumour oncolytic therapy with VSV and the interactions between macrophages and cytotoxic T cells, we consider a mathematical model that describes the time evolution of the following variables: the density of uninfected tumour cells (documentclass[12pt]{minimal}
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begin{document}$$x_{text {u}}$$end{document}xu), the density of virus-infected tumour cells (documentclass[12pt]{minimal}
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begin{document}$$x_{text {i}}$$end{document}xi), the density of virus particles (documentclass[12pt]{minimal}
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begin{document}$$x_{text {v}}$$end{document}xv), the density of M1 macrophages (documentclass[12pt]{minimal}
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begin{document}$$x_{text {m1}}$$end{document}xm1), the density of M2 macrophages (documentclass[12pt]{minimal}
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begin{document}$$x_{text {m2}}$$end{document}xm2) and the density of cytotoxic (effector) documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells (documentclass[12pt]{minimal}
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begin{document}$$x_{text {e}}$$end{document}xe); see also Fig. 1b. The time-evolution of these densities is described by the following equations: 1adocumentclass[12pt]{minimal}
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begin{document}$$begin{aligned} frac{dx_{text {u}}}{dt},=,&r x_{text {u}}left (1-frac{x_{text {u}}}{K} right )-d_{v}x_{text {v}}frac{x_{text {u}}}{h_{u}^{v}+x_{text {u}}}-d_{u}x_{text {u}}frac{x_{text {e}}}{h_{e}+x_{text {e}}}- d_{m1}x_{text {u}}frac{x_{text {m1}}}{h_{m}+x_{text {m2}}} \&+d_{m2}x_{text {u}}frac{x_{text {m2}}}{h_{m}+x_{text {m2}}}, end{aligned}$$end{document}dxudt=rxu1-xuK-dvxvxuhuv+xu-duxuxehe+xe-dm1xuxm1hm+xm2+dm2xuxm2hm+xm2,1bdocumentclass[12pt]{minimal}
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begin{document}$$begin{aligned} frac{dx_{text {i}}}{dt},=,&d_{v}x_{text {v}}frac{x_{text {u}}}{h_{u}^{v}+x_{text {u}}} -delta _{i} x_{text {i}}-d_{u}^{v}x_{text {i}}frac{x_{text {e}}}{h_{e}+x_{text {e}}} -d_{m1}^{v} x_{text {i}}frac{x_{text {m1}}}{h_{m}+x_{text {m2}}}, end{aligned}$$end{document}dxidt=dvxvxuhuv+xu-δixi-duvxixehe+xe-dm1vxixm1hm+xm2,1cdocumentclass[12pt]{minimal}
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begin{document}$$begin{aligned} frac{dx_{text {v}}}{dt},=,&H(t)+delta _{i} b x_{text {i}} -omega x_{text {v}} -d_{u}^{v}x_{text {v}}frac{x_{text {e}}}{h_{e}+x_{text {e}}} -d_{m1}^{v}x_{text {v}}frac{x_{text {m1}}}{h_{m}+x_{text {m2}}}, end{aligned}$$end{document}dxvdt=H(t)+δibxi-ωxv-duvxvxehe+xe-dm1vxvxm1hm+xm2,1ddocumentclass[12pt]{minimal}
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begin{document}$$begin{aligned} frac{dx_{text {m1}}}{dt},=,& a_{1}^{v} (x_{text {i}}+x_{text {v}})+a_{1}^{u}x_{text {u}}+p_{m1}x_{text {m1}}left (1-frac{x_{text {m1}}+x_{text {m2}}}{M} right )-x_{text {m1}} left(r_{m1}^{0}right. \& left. + r_{m1}^{u}frac{x_{text {u}}}{h_{u}+x_{text {u}}}right) + x_{text {m2}}left ( r_{m2}^{0} +r_{m2}^{v}frac{x_{text {v}}}{h_{v}+x_{text {v}}}right ) – d_{em1}x_{text {m1}}, end{aligned}$$end{document}dxm1dt=a1v(xi+xv)+a1uxu+pm1xm11-xm1+xm2M-xm1rm10+rm1uxuhu+xu+xm2rm20+rm2vxvhv+xv-dem1xm1,1edocumentclass[12pt]{minimal}
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begin{document}$$begin{aligned} frac{dx_{text {m2}}}{dt},=,&a_{2}^{u}x_{text {u}}+p_{m2}x_{text {m2}}left (1-frac{x_{text {m1}}+x_{text {m2}}}{M} right )+x_{text {m1}}left (r_{m1}^{0}+r_{m1}^{u}frac{x_{text {u}}}{h_{u}+x_{text {u}}}right) \ & -x_{text {m2}}left ( r_{m2}^{0} +r_{m2}^{v}frac{x_{text {v}}}{h_{v}+x_{text {v}}}right ) -d_{em2}x_{text {m2}}, end{aligned}$$end{document}dxm2dt=a2uxu+pm2xm21-xm1+xm2M+xm1rm10+rm1uxuhu+xu-xm2rm20+rm2vxvhv+xv-dem2xm2,1fdocumentclass[12pt]{minimal}
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begin{document}$$begin{aligned} frac{dx_{text {e}}}{dt}=&p_{e}frac{x_{text {m1}}}{h_{m}+x_{text {m2}} }-d_{ee}x_{text {e}}-d_{t}x_{text {u}}x_{text {e}}. end{aligned}$$end{document}dxedt=pexm1hm+xm2-deexe-dtxuxe. These equations incorporate the following biological assumptions:The uninfected tumour cells, described by Eq. (1a), proliferate logistically with rate r, up to a carrying capacity K. Here, we assume a logistic growth because various experimental studies showed evidence of a reduced rate of tumour growth at larger sizes; see, for example, Laird (1964), Looney et al. (1980), Guiot et al. (2003). Further, we assume that the virus particles infect, at a rate documentclass[12pt]{minimal}
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begin{document}$$d_{v}$$end{document}dv, only a certain proportion of the tumour (due to a multitude of obstacles associated with the tumour microenvironment  Wong et al. 2010). This can be modelled using a saturated term for the tumour–virus interactions, with documentclass[12pt]{minimal}
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begin{document}$$h_{u}^{v}$$end{document}huv the half saturation constant for tumour cells infected with the oncolytic virus particles. The uninfected tumour cells can be eliminated at a rate documentclass[12pt]{minimal}
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begin{document}$$gamma ^{+}$$end{document}γ+documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells. Note that the saturated term in (1a) for tumour elimination by documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells describes the fact that only a fraction of these cells are IFNdocumentclass[12pt]{minimal}
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begin{document}$$gamma$$end{document}γ positive—see also (Bridle et al. 2010). Moreover, we assume that the uninfected tumour cells can be eliminated by the M1 cells at a rate documentclass[12pt]{minimal}
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begin{document}$$d_{m1}$$end{document}dm1, since high numbers of infiltrating M1 macrophages are associated with good patient prognosis (Mantovani et al. 2006), and can eliminate mouse melanoma even in the absence of documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells (Hara et al. 1995). The presence of M2 cells inhibits the anti-tumour immune response generated by these M1 cells (Sica et al. 2008). Finally, we assume that these M2 cells support tumour growth at a rate documentclass[12pt]{minimal}
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begin{document}$$d_{m2}$$end{document}dm2, through the pro-tumour cytokines they secrete (Allavena and Mantovani 2012).The virus-infected tumour cells, described by Eq. (1b), die at a rate documentclass[12pt]{minimal}
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begin{document}$$delta _{i}$$end{document}δi following viral replication and cell burst (see Eq. (1c)). The infected cells can be detected and eliminated at a rate documentclass[12pt]{minimal}
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begin{document}$$d_{m1}^{v}$$end{document}dm1v(documentclass[12pt]{minimal}
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begin{document}$$gg d_{m1}$$end{document}≫dm1) by the M1 macrophages (Hashimoto et al. 2007; Italiani and Boraschi 2014), or at a rate documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells (Bridle et al. 2010). The anti-viral effect of M1 cells is inhibited by the presence of M2 cells.The virus, described by Eq. (1c), is injected into the system at some time documentclass[12pt]{minimal}
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begin{document}$$t>0$$end{document}t>0, and this virus administration is described by a function H(t) that is usually a combination of Heaviside functions; see caption of Fig. 2 for the description of H(t). The number of viral particles inside the tumour increases following the fast replication of these particles inside the tumour cells, causing the cells to burst open and release the particles. We denote by b the burst size, i.e., the number of viral particles released by one infected tumour cell. The half-life of these viral particles is documentclass[12pt]{minimal}
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begin{document}$$1/omega$$end{document}1/ω (with non-immune human and mouse serum neutralising VSV very quickly  Tesfay et al. 2013). Moreover, the M1 macrophages can promote an anti-viral immune response, which leads to early clearance of virus particles at a rate documentclass[12pt]{minimal}
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begin{document}$$d_{u}^{v}$$end{document}duv, e.g., through cytokine-mediated inhibition of viral replication (Komatsu et al. 1999; Christensen et al. 2004). We note that the rate at which the documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+T cells lyse the virus-infected cells could be different from the rate at which the virus particles are eliminated. For now we assume that both events are described by the same rate documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells elimination rates for the virus-infected cells and for the virus particles.The M1 macrophages, described by Eq. (1d), are activated, at a rate documentclass[12pt]{minimal}
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begin{document}$$gamma$$end{document}γ) (Labonte et al. 2014). This immune response could also be activated, at a small rate documentclass[12pt]{minimal}
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begin{document}$$a_{1}^{u}$$end{document}a1u, by the uninfected tumour cells—if the macrophages could detect these tumour cells. The recruitment of M1 macrophages to the tumour site occurs at an average rate documentclass[12pt]{minimal}
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begin{document}$$rightarrow$$end{document}→M2 re-polarisation of macrophages occurs: (i) at a small constant rate documentclass[12pt]{minimal}
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begin{document}$$beta$$end{document}β, which can be produced by different types of healthy and immune cells), and (ii) at a tumour-dependent rate documentclass[12pt]{minimal}
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begin{document}$$hbox {M2}rightarrow hbox {M1}$$end{document}M2→M1 macrophages occurs at a small constant rate documentclass[12pt]{minimal}
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begin{document}$$gamma$$end{document}γ or IL-12 produced by different types of cells in the environment). Recent experimental studies have shown that oncolytic viruses can be genetically modified to carry chemokines and cytokines that can induce a documentclass[12pt]{minimal}
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begin{document}$$r_{m2}^{v}>0$$end{document}rm2v>0 will be discussed in Sect. 3.3. Finally, the M1 macrophages have a death rate of documentclass[12pt]{minimal}
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begin{document}$$d_{em1}$$end{document}dem1 (Yang et al. 2014; Italiani and Boraschi 2014).The M2 macrophages, described by Eq. (1e), are activated at a rate documentclass[12pt]{minimal}
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begin{document}$$a_{2}^{u}$$end{document}a2u by cytokines such as IL-4, IL-10, IL-13, TGF-documentclass[12pt]{minimal}
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begin{document}$$beta$$end{document}β, which are usually associated with a tumour-promoting environment (Labonte et al. 2014). These macrophages proliferate logistically at an average rate documentclass[12pt]{minimal}
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begin{document}$$leftrightarrow$$end{document}↔M1 re-polarisation rates have been discussed in the previous paragraph. The M2 macrophages have a death rate of documentclass[12pt]{minimal}
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begin{document}$$1/d_{em2}$$end{document}1/dem2. Since many experimental studies on the turnover of macrophages do not distinguish between the M1 and M2 cells, throughout most of this study we will assume that documentclass[12pt]{minimal}
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begin{document}$$d_{em1}=d_{em2}:=d_{em}$$end{document}dem1=dem2:=dem. The cases where documentclass[12pt]{minimal}
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begin{document}$$d_{em1}ne d_{em2}$$end{document}dem1≠dem2 and documentclass[12pt]{minimal}
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begin{document}$$p_{m1}ne p_{m2}$$end{document}pm1≠pm2 will be investigated in Sect. 3.1, in the context of sensitivity analysis.The cytotoxic documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells, described by Eq. (1e), are activated and proliferate at a rate documentclass[12pt]{minimal}
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begin{document}$$p_{e}$$end{document}pe in the presence of tumour and viral antigens presented by M1 macrophages (Pozzi et al. 2005; Olazabal et al. 2008). (We acknowledge that both dendritic cells (DCs) and macrophages can prime naive documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells (Pozzi et al. 2005), with the DCs being considered the most potent antigen-presenting cells. However in this study we focus only on the macrophages since they are very abundant inside the tumour microenvironment, and thus they likely contribute to the initiation of T cell immunity. Moreover, the explicit inclusion of DCs in the model would only increase the complexity of the current system.) In contrast to other modelling studies on tumour–immune interactions following VSV therapy (see Macnamara and Eftimie 2015), here we assume that the tumour cells or virus particles do not influence directly the adaptive immune response, but they act through the innate response (M1 cells) which then activate the T cells. This is biologically realistic as experimental studies have shown that macrophage depletion suppressed the priming of documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells (Ciavarra et al. 2000). Finally, the documentclass[12pt]{minimal}
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begin{document}$$hbox {CD8}^{+}$$end{document}CD8+ T cells have a natural death rate documentclass[12pt]{minimal}
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begin{document}$$d_{e}$$end{document}de, and are inactivated by the tumour cells at a rate documentclass[12pt]{minimal}
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begin{document}$$d_{t}$$end{document}dt.

In the following we start the investigation into the role of macrophages on oncolytic virotherapies by performing first a local sensitivity analysis, to identify those parameters to which the model is most sensitive and to see which of these parameters are important in macrophages polarisation. Then we focus on a few virus-related and immune-related parameters (some identified as important during the sensitivity analysis), which will be varied to reproduce different experimental and clinical approaches aimed at controlling tumour growth. In this context, we will discuss the effect of varying these parameters on the size of M1 and M2 populations, and how this correlates with tumour control/elimination. This investigation will address mainly question (I) from the Introduction. To address questions (II) and (III) we will combine numerical simulations for transient system dynamics with steady-state analysis of long-term dynamics.

In this study we introduced a mathematical model for the investigation of the interactions between melanoma tumour cells, an oncolytic Vesicular Stomatitis Virus (VSV) that was administered twice in 3 days, and innate and adaptive immune responses. We first parametrised the model without the oncolytic virus by fitting it to baseline experimental data in Chen et al. (2011), which focused on the anti-tumour/pro-tumour immune response of the M1 and M2 macrophages. Then, we fixed the tumour and immune-related parameters, and fit the full model with the oncolytic virus (VSV) to the baseline experimental data in Fernandez et al. (2002). To ensure a better model-to-data fit, we incorporated the assumption of higher anti-tumour immune responses following the first viral infection, which leads to the release of TAAs, PAMPs and DAMPs by destroyed tumour cells. For the parameters shown in Table 1, the anti-tumour immune responses following the VSV injection (documentclass[12pt]{minimal}
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begin{document}$$d_{u}^{t>15}=0.85$$end{document}dut>15=0.85, documentclass[12pt]{minimal}
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begin{document}$$d_{m1}^{t>11}=0.29$$end{document}dm1t>11=0.29) are much greater than the anti-tumour immune responses before VSV injection (documentclass[12pt]{minimal}
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begin{document}$$d_{u}^{t<15}=0.44$$end{document}dut<15=0.44, documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$d_{m1}^{t<11}=0.01$$end{document}dm1t<11=0.01). However, since the value of the anti-tumour immune response following VSV injection (documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$d_{u}^{t>15}$$end{document}dut>15, documentclass[12pt]{minimal}
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begin{document}$$d_{m1}^{t>11}$$end{document}dm1t>11) depends on the multitude of fixed tumour and immune parameters (identified through fitting the data in Chen et al. (2011)), and since it is likely that one can find multiple sets of tumour and immune parameters that can fit the data in Chen et al. (2011), we expect that it is possible to find also lower immune responses that fit the data in Fernandez et al. (2002). However, this sort of parameter investigation was not the aim of this current study. Rather, our goal was to investigate whether we can use only one class of mathematical models to reproduce and explain the dynamics suggested by data generated by two different experimental systems, and to further investigate the overall model dynamics. A global parameter optimisation, which can be used to fit at the same time multiple different experiments, will be the subject of a different study. We should emphasise here that despite the possibility of having different sets of parameter values that fit the same data, we would not expect significant changes in the overall dynamics of the system (1) – see also Figs. 5, 6, 7.

The linear stability of the steady states documentclass[12pt]{minimal}
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begin{document}$$(x_{text {u}},x_{text {i}},x_{text {v}},x_{text {m1}},x_{text {m2}},x_{text {e}})$$end{document}(xu,xi,xv,xm1,xm2,xe) is given by the eigenvalues of the Jacobian matrix (J) associated with system (1):8documentclass[12pt]{minimal}
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begin{document}$$begin{aligned} J=left( begin{array}{cccccc} a_{11} &{} a_{12} &{} a_{13} &{} a_{14} &{} a_{15} &{} a_{16}\ a_{21} &{} a_{22} &{} a_{23} &{} a_{24} &{} a_{25} &{} a_{26}\ 0 &{} a_{32} &{} a_{33} &{} a_{34} &{} a_{35} &{} a_{36}\ a_{41} &{} a_{42} &{} a_{43} &{} a_{44} &{} a_{45} &{} 0\ a_{51} &{} 0 &{} a_{53} &{} a_{54} &{} a_{55} &{} 0\ a_{61} &{} 0 &{} 0 &{} a_{14} &{} a_{15} &{} a_{16}\ end{array} right) , ;; text {with};; a_{ij}ge 0, end{aligned}$$end{document}J=a11a12a13a14a15a16a21a22a23a24a25a260a32a33a34a35a36a41a42a43a44a450a510a53a54a550a6100a14a15a16,withaij≥0,and documentclass[12pt]{minimal}
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begin{document}$$a_{i,j}$$end{document}ai,j the terms obtained after differentiating the right-hand-sides of Eq. (1) with respect to the model variables.

 

Source:

http://doi.org/10.1007/s10441-019-09357-9

 

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