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

Ali Raza,Muhammad Rafiq,Jan Awrejcewicz,Nauman Ahmed,Muhammad Mohsin

doi:10.3390/math10030368

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.

Highlights

Cancer is a family of diseases associated with developing abnormal cells to seize or transmit to other parts of one’s body
Cancer is the rapid emergence of abnormal cells which arise outside their normal limits, and it may occupy the linked parts of the body and transfer to the tissues afterward
Abernathy et al investigated the dynamics of the cell population, including interactions between infected and uninfected brain tumor cells [5]

Summary

Introduction

Cancer is a family of diseases associated with developing abnormal cells to seize or transmit to other parts of one’s body. Tuwairqi et al presented the qualitative analysis of cancer cells in the cell population [1]. In 2020, Nouni et al analyzed the tumor cells’ dynamics for the immune response of a virological model for cancer therapy [3]. Storey et al developed a deterministic model for treating a tumor via oncolytic treatment [4]. Malinzi et al presented the wave propagation model for dynamics of chemo/virotherapy cancer [8]. Timalsina et al developed computational techniques to model tumor virotherapy in the cell population [10]. Rommeifanger et al developed a melanoma tumor model in the cell dynamics and performed its qualitative analysis [11]. Liu et al launched a comparison analysis of a deterministic and stochastic model for tumor-immune responses to chemotherapy [12].

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