Quantitative impact of immunomodulation versus oncolysis with cytokine-expressing virus therapeutics
Peter S. Kim Joseph J. Crivelli Il-Kyu Choi Chae-Ok Yun Joanna R. Wares
Mathematical Biosciences & Engineering 2015, 12(4): 841-858 doi: 10.3934/mbe.2015.12.841
The past century's description of oncolytic virotherapy as a cancer treatment involving specially-engineered viruses that exploit immune deficiencies to selectively lyse cancer cells is no longer adequate. Some of the most promising therapeutic candidates are now being engineered to produce immunostimulatory factors, such as cytokines and co-stimulatory molecules, which, in addition to viral oncolysis, initiate a cytotoxic immune attack against the tumor.
    This study addresses the combined effects of viral oncolysis and T-cell-mediated oncolysis. We employ a mathematical model of virotherapy that induces release of cytokine IL-12 and co-stimulatory molecule 4-1BB ligand. We found that the model closely matches previously published data, and while viral oncolysis is fundamental in reducing tumor burden, increased stimulation of cytotoxic T cells leads to a short-term reduction in tumor size, but a faster relapse.
    In addition, we found that combinations of specialist viruses that express either IL-12 or 4-1BBL might initially act more potently against tumors than a generalist virus that simultaneously expresses both, but the advantage is likely not large enough to replace treatment using the generalist virus. Finally, according to our model and its current assumptions, virotherapy appears to be optimizable through targeted design and treatment combinations to substantially improve therapeutic outcomes.
keywords: co-stimulatory molecules adenovirus ordinary differential equations model. mathematical model cytokines Oncolytic virotherapy
Stability crossing boundaries of delay systems modeling immune dynamics in leukemia
Silviu-Iulian Niculescu Peter S. Kim Keqin Gu Peter P. Lee Doron Levy
Discrete & Continuous Dynamical Systems - B 2010, 13(1): 129-156 doi: 10.3934/dcdsb.2010.13.129
This paper focuses on the characterization of delay effects on the asymptotic stability of some continuous-time delay systems encountered in modeling the post-transplantation dynamics of the immune response to chronic myelogenous leukemia. Such models include multiple delays in some large range, from one minute to several days. The main objective of the paper is to study the stability of the crossing boundaries of the corresponding linearized models in the delay-parameter space by taking into account the interactions between small and large delays. Weak, and strong cell interactions are discussed, and analytic characterizations are proposed. An illustrative example together with related discussions completes the presentation.
keywords: leukemia models. Delay asymptotic stability switch crossing curves reversal quasipolynomial
Treatment strategies for combining immunostimulatory oncolytic virus therapeutics with dendritic cell injections
Joanna R. Wares Joseph J. Crivelli Chae-Ok Yun Il-Kyu Choi Jana L. Gevertz Peter S. Kim
Mathematical Biosciences & Engineering 2015, 12(6): 1237-1256 doi: 10.3934/mbe.2015.12.1237
Oncolytic viruses (OVs) are used to treat cancer, as they selectively replicate inside of and lyse tumor cells. The efficacy of this process is limited and new OVs are being designed to mediate tumor cell release of cytokines and co-stimulatory molecules, which attract cytotoxic T cells to target tumor cells, thus increasing the tumor-killing effects of OVs. To further promote treatment efficacy, OVs can be combined with other treatments, such as was done by Huang et al., who showed that combining OV injections with dendritic cell (DC) injections was a more effective treatment than either treatment alone. To further investigate this combination, we built a mathematical model consisting of a system of ordinary differential equations and fit the model to the hierarchical data provided from Huang et al. We used the model to determine the effect of varying doses of OV and DC injections and to test alternative treatment strategies. We found that the DC dose given in Huang et al. was near a bifurcation point and that a slightly larger dose could cause complete eradication of the tumor. Further, the model results suggest that it is more effective to treat a tumor with immunostimulatory oncolytic viruses first and then follow-up with a sequence of DCs than to alternate OV and DC injections. This protocol, which was not considered in the experiments of Huang et al., allows the infection to initially thrive before the immune response is enhanced. Taken together, our work shows how the ordering, temporal spacing, and dosage of OV and DC can be chosen to maximize efficacy and to potentially eliminate tumors altogether.
keywords: ordinary differential equations model. co-stimulatory molecules Oncolytic virotherapy cytokines mathematical model adenovirus
Stability of travelling waves in a Wolbachia invasion
Matthew H. Chan Peter S. Kim Robert Marangell
Discrete & Continuous Dynamical Systems - B 2018, 23(2): 609-628 doi: 10.3934/dcdsb.2018036

Numerous studies have examined the growth dynamics of Wolbachia within populations and the resultant rate of spatial spread. This spread is typically characterised as a travelling wave with bistable local growth dynamics due to a strong Allee effect generated from cytoplasmic incompatibility. While this rate of spread has been calculated from numerical solutions of reaction-diffusion models, none have examined the spectral stability of such travelling wave solutions. In this study we analyse the stability of a travelling wave solution generated by the reaction-diffusion model of Chan & Kim [4] by computing the essential and point spectrum of the linearised operator arising in the model. The point spectrum is computed via an Evans function using the compound matrix method, whereby we find that it has no roots with positive real part. Moreover, the essential spectrum lies strictly in the left half plane. Thus, we find that the travelling wave solution found by Chan & Kim [4] corresponding to competition between Wolbachia-infected and -uninfected mosquitoes is linearly stable. We employ a dimension counting argument to suggest that, under realistic conditions, the wavespeed corresponding to such a solution is unique.

keywords: Population dynamics Evans function stability analysis Wolbachia

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