Mathematical Modeling of Leukemia within Stochastic Fractional Delay Differential Equations

In 2022, Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer (IARC). Leukemia is still a threat and challenge for all regions because of 46.6% infection in Asia, and 22.1% and 14.7% infection rates in Europe and North America, respectively. To study the dynamics of Leukemia, the population of cells has been divided into three subpopulations of cells susceptible cells, infected cells, and immune cells. To investigate the memory effects and uncertainty in disease progression, leukemia modeling is developed using stochastic fractional delay differential equations (SFDDEs). The feasible properties of positivity, boundedness, and equilibria (i.e., Leukemia Free Equilibrium (LFE) and Leukemia Present Equilibrium (LPE)) of the model were studied rigorously. The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated. To support the theoretical analysis of the model, the Grunwald Letnikov Nonstandard Finite Difference (GL-NSFD) method was used to simulate the results of each subpopulation with memory effect. Also, the positivity and boundedness of the proposed method were studied. Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.