Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
25 January 2020 |
09 February 2020 |
10 March 2020 |
Abstract: Nowadays, cancer is among the leading causes of death worldwide. To combat this dangerous disease, we can treat it with oncolytic virotherapy which uses viruses programmed to infect and kill cancer cells without causing damage to normal tissue. In this work, we propose a mathematical model with time delay that describes the dynamics of cancer treatment with oncolytic viruses. In the proposed model, the infection transmission process is modeled by Hattaf-Yousfi functional response which covers various types of incidence rate existing in the literature. We first show that our model is biologically and mathematically well-posed. Also, we prove the existence of three equilibrium points which represent the desired outcome of therapy, the partial success of treatment and the failure of treatment. Moreover, we establish the stability of the three equilibria and the local existence of Hopf bifurcation.
