Stochastic Analysis of Nonlinear Cancer Disease Model through Virotherapy and Computational Methods

Ali Raza, Jan Awrejcewicz, Muhammad Rafiq, Nauman Ahmed and Muhammad Mohsin
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Ali Raza: Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore 54000, Pakistan
Jan Awrejcewicz: Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, Poland
Muhammad Rafiq: Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore 54000, Pakistan
Nauman Ahmed: Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan
Muhammad Mohsin: Department of Mathematics, Chemnitz University of Technology, 09111 Chemnitz, Germany

Mathematics, 2022, vol. 10, issue 3, 1-18

Abstract: Cancer is a common term for many diseases that can affect anybody. A worldwide leading cause of death is cancer, according to the World Health Organization (WHO) report. In 2020, ten million people died from cancer. This model identifies the interaction of cancer cells, viral therapy, and immune response. In this model, the cell population has four parts, namely uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). This study presents the analysis of the stochastic cancer virotherapy model in the cell population dynamics. The model results have restored the properties of the biological problem, such as dynamical consistency, positivity, and boundedness, which are the considerable requirements of the models in these fields. The existing computational methods, such as the Euler Maruyama, Stochastic Euler, and Stochastic Runge Kutta, fail to restore the abovementioned properties. The proposed stochastic nonstandard finite difference method is efficient, cost-effective, and accommodates all the desired feasible properties. The existing standard stochastic methods converge conditionally or diverge in the long run. The solution by the nonstandard finite difference method is stable and convergent over all time steps.

Keywords: cancer model; stochastic differential equations; computational methods; stability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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