Stochastic model analysis of cancer oncolytic virus therapy: estimation of the extinction mean times and their probabilities

• Published in: Nonlinear dynamics 2022-02, Vol.107 (3), p.2819-2846
• Main Authors: Camara, B. I., Mokrani, H., Diouf, A., Sané, I., Diallo, A. S.
• Format: Article
• Language: English
• Subjects: Algorithms; Automotive Engineering; Cancer; Classical Mechanics; Control; Depletion; Differential equations; Diffusion rate; Dynamical Systems; Engineering; Extinction; Immunotherapy; Lymphocytes; Mechanical Engineering; Original Paper; Parameter sensitivity; Robustness (mathematics); Stochastic models; Stochastic systems; Toxicity; Tumors; Vibration; Viruses
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-07074-y

In this paper, we propose a mathematical model on the oncolytic virotherapy incorporating virus-specific cytotoxic T lymphocyte (CTL) response, which contribute to killing infected tumor cells. In order to improve the understanding of the dynamic interactions between tumor cells and virus-specific CTLs, stochastic differential equation models are constructed. We obtain sufficient conditions for existence, persistence and extinction of the stochastic system. In relation to the therapy control, we also analyze the stochasticity role of equilibrium point stabilities. The Monte Carlo algorithm is used to estimate the mean extinction time and the extinction probability of cancer cells or viruses-specific CTLs. Our simulations highlighted the switch of the system leaving the attractor basin of the three species co-existence equilibrium toward that of cancer cell extinction or that of virus-specific CTLs depletion. This allowed us to characterize the spaces of cancer control parameters. Finally, we determine the model solution robustness by analyzing the sensitivity of the model characteristic parameters. Our results demonstrate the high dependence of the virotherapy success or failure on the combination of stochastic diffusion parameters with the maximum per capita growth rate of uninfected tumor cells, the transmission rate, the viral cytotoxicity and the strength of the CTL response.