Modeling dynamics of cancer virotherapy with immune response

Abstract

Virotherapy is a therapeutic treatment for cancer. It uses genetically engineered viruses to selectively infect, replicate in, and destroy cancer cells without damaging normal cells. In this paper, we present a modified model to include, within the dynamics of virotherapy, the interaction between uninfected tumor cells and immune response. The model is analyzed qualitatively to produce five equilibrium points. One of these equilibriums demonstrates the effect observed in virotherapy, where the immune system demolishes infected cells as well as viruses. Moreover, the existence and stability of the equilibrium points are established under certain criteria. Numerical simulations are performed to display the agreement with the analytical results. Finally, parameter analysis is carried out to illustrate which parameters in the model affect the outcome of virotherapy.

Mechanistic Modeling of a Novel Oncolytic Virus, V937, to Describe Viral Kinetic and Dynamic Processes Following Intratumoral and Intravenous Administration

“…Various mathematical models to characterize in vitro viral dynamics (Bagheri et al, 2011;Titze et al, 2017), in vivo behavior limited to tumor size metrics (Bajzer et al, 2008;Eftimie et al, 2011), theoretical frameworks (Wein et al, 2003;Mok et al, 2009;Paiva et al, 2009;Malinzi et al, 2017;Jenner et al, 2018;Cassidy and Humphries, 2019;Al-Tuwairqi et al, 2020) and develop predictive in-silico trials (Jenner et al, 2021) have been so far described. To the best of our knowledge, the integration of kinetic parameters including viral distribution to tumor lesions and comparing i. t. and i. v. administrations has not yet been addressed.…”

A mathematical study of the role of tBregs in breast cancer

“…It is easy to see that the conditions of the Picard-Lindelöf theorem are fulfilled, since every function of the right-hand side of system (2) is continuous, just like its partial derivative with respect to every variable. Thus, we have that there exists a unique solution to problem (2)- (3). In fact, we can extended the solution and consider it in the maximal non-negative interval of existence.…”

“…T yields θ B m T > 1 b , whereas choosing the value m B T yields θ B m T < 1 b , allowing us to explore the different dynamics of problem ( 2)- (3).…”

“…The theory of ordinary differential equations and dynamical systems has been deployed by scientists in order to gain new insights about the complex interactions between cancer and the immune system. To this end, several models have been constructed for the study of different entities concerning cancer-immune interactions such as cancer cells, normal cells, cytolytic cells, regulatory cells, cytokines, cancer cells at different stages as well as various therapies [25,29,12,44,8,24,26,14,3,39].…”

Modeling dynamics of fast food and obesity for evaluating the peer pressure effect and workout impact

“…Most previous studies have examined the obesity models numerically due to their complexity. However, qualitative analysis of mathematical models [9,12,18,28] presents more general results and allows for better understanding of the critical parameters that play a significant role in the dynamics of the models, see for example [1][2][3]19].…”