Treating cancerous cells with viruses: insights from a minimal model for oncolytic virotherapy

Abstract

In recent years, interest in the capability of virus particles as a treatment for cancer has increased. In this work, we present a mathematical model embodying the interaction between tumour cells and virus particles engineered to infect and destroy cancerous tissue. To quantify the effectiveness of oncolytic virotherapy, we conduct a local stability analysis and bifurcation analysis of our model. In the absence of tumour growth or viral decay, the model predicts that oncolytic virotherapy will successfully eliminate the tumour cell population for a large proportion of initial conditions. In comparison, for growing tumours and decaying viral particles there are no stable equilibria in the model; however, oscillations emerge for certain regions in our parameter space. We investigate how the period and amplitude of oscillations depend on tumour growth and viral decay. We find that higher tumour replication rates result in longer periods between oscillations and lower amplitudes for uninfected tumour cells. From our analysis, we conclude that oncolytic viruses can reduce growing tumours into a stable oscillatory state, but are insufficient to completely eradicate them. We propose that it is only with the addition of other anti-cancer agents that tumour eradication may be achieved by oncolytic virus. ARTICLE HISTORY

Modeling the Spatiotemporal Dynamics of Oncolytic Viruses and Radiotherapy as a Treatment for Cancer

“…It should be noted that our model is similar to the one in [12], where the new addition of terms involves the reduction of free virus density due to the infection of tumor cells. We have also incorporated the spatial variation of the variables due to the diffusion of the drug and cancer cells.…”

“…Jenner et al [12] introduced a mathematical model consisting of three nonlinear ODEs describing the interaction between tumor cells and oncolytic virus therapy. In this paper, we will develop these ODEs by considering the spatial variation and diffusion of cancer cells.…”

Um Modelo Matemático Fracionário de Viroterapia no Tratamento de Tumores Agressivos

“…Jenner e Coster [10] propõem o modelo a seguir com três equações diferenciais ordinárias para o tratamento de um tumor agressivo através de terapia com vírus oncolítico. Seja o seguinte sistema de equações diferenciais ordinárias…”

“…Biologicamente, esse crescimento exponencial do tumoré inviável devidoàs limitações de nutrientes e espaço. Contudo, o crescimento exponencial ainda pode ser visto como uma aproximação suficiente para o crescimento do tumor sob tratamento com um vírus oncolítico, já que a escala de tempo da interação entre partículas de vírus e células tumoraisé curta [10]. A taxa de infecção da população de células tumorais não infectadasé proporcional ao produto das populações de vírus e células tumorais e que este ocorre com taxa β [12].…”

“…d v representa a taxa de mortalidade das partículas virais. O modelo (1) adimensionalizadoé dado por [10]…”