Dynamic analysis of stochastic modeling of tumor-macrophage interactions incorporating multiplicative and additive noises.

In this study, we investigate the dynamic mechanisms of tumor progression in response to fluctuations and uncertainties within the tumor-immune microenvironment. Utilizing temporal single-cell data, we develop a novel stochastic reaction-convection model that captures the spatiotemporal dynamics of macrophage responses to tumor cells subjected to both multiplicative and additive noise generated by non-homologous microenvironmental fluctuations. We prove the existence and uniqueness of a global positive solution for the proposed stochastic model. Then, by combining the stochastic Lyapunov analysis and the comparison theorem, we explore the moment boundaries for cell populations, as well as the asymptotic behavior at the boundary equilibrium points; sufficient conditions for driving sustained tumor growth and clearance are derived by employing the ergodicity theorem and are interestingly found to be only related to multiplicative noise. Furthermore, we employ an upwind finite difference scheme to simulate the effects of different noise types on a cell population distribution and the persistence of tumor growth. Results show that while additive noise influences the multimodal distribution of early tumor cell phenotypes, it has minimal impact on the mean density of tumor cells, indicating that additive noise acts primarily as a diffusion factor. In contrast, increasing multiplication noise effectively inhibits the development without altering the number of peaks in a phenotypic distribution. Interestingly, when additive and multiplicative noises are correlated, stronger additive noise can have dual effects on the steady-state distribution of tumor cells, with increased correlation positively influencing tumor cell elimination. These results provide novel insight into the tumor-immune microenvironment dynamics.