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The AIDS is a chronic disease and the researchers still exert their high efforts to reach the cure of HIV infection. The most common treatment is the antiretroviral therapy (cART) and the virus can be more effected if the patients stop using cART. The other problem is that the CD8+ T cells might be exhausted by persistent immune activation by cART. This paper introduces fractional-order into a mathematical model of HIV infection combining with stem cell therapy and control the infection by the immune system cells (CD8+ T cells). The paper introduced the numerical solutions for the mathematical model. The results show that the stem cell therapy with the activation of immune system cells might causes the cure for a HIV patient. This results are consistent with medical studies. Also, we proposed the effect of the fractional order (α) on the figures of the components. [ABSTRACT FROM AUTHOR]

Simple Summary: Immune checkpoint inhibitors (ICIs) are cancer immunotherapeutics that reinvigorate immune cells' ability to attack tumor cells. Despite remarkable results in some patients, ICIs do not demonstrate the same efficacy across all individuals. In this study, we present the first side-by-side comparison of an agent-based model (ABM) with an ordinary differential equation (ODE) model for ICIs targeting the PD-1/PD-L1 immune checkpoint. We consider tumor cells of high and low antigenicity and two distinct immune-cell kill mechanisms. Using key parameters calibrated from mouse bladder cancer studies, we simulate virtual tumors using both models. Our research identifies crucial tumor-immune characteristics that influence the efficacy of ICIs. By exploring the unique spatial insights provided by the ABM, we underscore the importance of considering the spatial complexity of the tumor microenvironment in mathematical models of ICIs, potentially paving the way for more effective cancer treatments. Since the introduction of the first immune checkpoint inhibitor (ICI), immunotherapy has changed the landscape of molecular therapeutics for cancers. However, ICIs do not work equally well on all cancers and for all patients. There has been a growing interest in using mathematical and computational models to optimize clinical responses. Ordinary differential equations (ODEs) have been widely used for mechanistic modeling in immuno-oncology and immunotherapy. They allow rapid simulations of temporal changes in the cellular and molecular populations involved. Nonetheless, ODEs cannot describe the spatial structure in the tumor microenvironment or quantify the influence of spatially-dependent characteristics of tumor-immune dynamics. For these reasons, agent-based models (ABMs) have gained popularity because they can model more detailed phenotypic and spatial heterogeneity that better reflect the complexity seen in vivo. In the context of anti-PD-1 ICIs, we compare treatment outcomes simulated from an ODE model and an ABM to show the importance of including spatial components in computational models of cancer immunotherapy. We consider tumor cells of high and low antigenicity and two distinct cytotoxic T lymphocyte (CTL) killing mechanisms. The preferred mechanism differs based on the antigenicity of tumor cells. Our ABM reveals varied phenotypic shifts within the tumor and spatial organization of tumor and CTLs despite similarities in key immune parameters, initial simulation conditions, and early temporal trajectories of the cell populations. [ABSTRACT FROM AUTHOR]