Dynamics of Tumor-Immune System with Random Noise

Fathalla A. Rihan and Chinnathambi Rajivganthi
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Fathalla A. Rihan: Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, United Arab Emirates
Chinnathambi Rajivganthi: School of Applied Mathematics, Getulio Vargas Foundation, Rio de Janeiro 22250-900, Brazil

Mathematics, 2021, vol. 9, issue 21, 1-14

Abstract: With deterministic differential equations, we can understand the dynamics of tumor-immune interactions. Cancer-immune interactions can, however, be greatly disrupted by random factors, such as physiological rhythms, environmental factors, and cell-to-cell communication. The present study introduces a stochastic differential model in infectious diseases and immunology of the dynamics of a tumor-immune system with random noise. Stationary ergodic distribution of positive solutions to the system is investigated in which the solution fluctuates around the equilibrium of the deterministic case and causes the disease to persist stochastically. In some conditions, it may be possible to attain infection-free status, where diseases die out exponentially with a probability of one. Some numerical simulations are conducted with the Euler–Maruyama scheme in order to verify the results. White noise intensity is a key factor in treating infectious diseases.

Keywords: infectious diseases; cancer-immune system; steady states; random noise; stochastic differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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