Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Abstract

Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic nonlinear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug. The analysis of the model is carried out for both the temporal and spatiotemporal cases. Travelling wave solutions to the spatiotemporal model are used to determine the minimum wave speed of tumour invasion. A sensitivity analysis is performed on the model parameters to establish the key parameters that promote cancer remission during chemovirotherapy treatment. Model analysis of the temporal model suggests that virus burst size and virus infection rate determine the success of the virotherapy treatment, whereas travelling wave solutions to the spatiotemporal model show that tumour diffusivity and growth rate are critical during chemovirotherapy. Simulation results reveal that chemovirotherapy is more effective and a good alternative to either chemotherapy or virotherapy, which is in agreement with the recent experimental studies. ARTICLE HISTORY

Multiscale modelling of cancer response to oncolytic viral therapy

“…The use of mathematical models to understand the temporal and spatio-temporal dynamics of viruses (including oncolytic viruses) has seen great developments over the last three decades [7,8,9,10,11,12,13]. While the majority of these models focused on the temporal dynamics of oncolytic viruses (mainly due to the availability of temporal data) [14,15,16,17,18,19,20,21,22,23], more recent advances in tumour imaging generated data on the spatial spread of tumours and viruses, which then led to the development of different mathematical models investigating the spatial spread of these viruses [21,23,24,25,26,27].…”

A Cellular Automata Model of Oncolytic Virotherapy in Pancreatic Cancer

“…The resulting behavior depends on the input parameters, which represent the biological circumstances around the tumor. Malinzi et al (2017) developed a partial differential equation-based model for oncolytic virotherapy. For the one-dimensional case, they assessed the stability of traveling wave solutions and the rate of tumor progression by means of the minimal traveling wave speed.…”

A mathematical model of viral oncology as an immuno-oncology instigator

“…Mathematical models have been used extensively to understand and predict tumour growth and tumourimmune interactions (see Santiago et al [2017]; Walker and Enderling [2016]; Wodarz [2016] for reviews). Existing models range from formulations as ordinary dierential equations (ODEs) [Idema et al, 2010;Kim et al, 2015;Kirschner and Panetta, 1998;MacNamara and Eftimie, 2015], to partial dierential equations [Hillen et al, 2013;Malinzi et al, 2017] and discrete DDEs [Liu et al, 2007;Mahasa et al, 2017;Villasana and Radunskaya, 2003]. Crivelli et al [2012] developed and analysed a discrete DDE model of tumour growth and viral oncology.…”