Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy.

Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy. Comput Math Methods Med. 2019;2019:1732815 Authors: El Alami Laaroussi A, Hia ME, Rachik M, Ghazzali R Abstract Despite advanced discoveries in cancerology, conventional treatments by surgery, chemotherapy, or radiotherapy remain ineffective in some situations. Oncolytic virotherapy, i.e., the involvement of replicative viruses targeting specific tumor cells, opens new perspectives for better management of this disease. Certain viruses naturally have a preferential tropism for the tumor cells; others are genetically modifiable to present such properties, as the lytic cycle virus, which is a process that represents a vital role in oncolytic virotherapy. In the present paper, we present a mathematical model for the dynamics of oncolytic virotherapy that incorporates multiple time delays representing the multiple time periods of a lytic cycle. We compute the basic reproductive ratio R 0, and we show that there exist a disease-free equilibrium point (DFE) and an endemic equilibrium point (DEE). By formulating suitable Lyapunov function, we prove that the disease-free equilibrium (DFE) is globally asymptotically stable if R 0 < 1 and unstable otherwise. We also demonstrate that under additional conditions, the endemic equilibrium is stable. Also, a Hopf bifurcation analysis of our dynamic system is used to understand how solutions and their stabilit...
Source: Computational and Mathematical Methods in Medicine - Category: Statistics Tags: Comput Math Methods Med Source Type: research