In this paper, we developed a mathematical model to describethe dynamics of Aflatoxins in plants, animals, and humans. Fourequilibrium points were found, and their stability analyses wereconducted using threshold quantities. If both are less than one, thestandardized toxic limit is not exceeded, while if both are greater thanone it is exceeded in both animals and humans. Standardized toxic limitis exceeded in a relevant host (animals or humans) when their respectivethreshold quantity is greater than one. Numerical simulations werecarried out to support the analytic results. The need to use experimentaldata in the model is also shown. This could ease satisfactoryharmonization of acceptable standards and facilitate international tradeof food and feeds.

This paper aims to study the dynamics of immune suppressors/checkpoints, immune system, and BCG in the treatment of superficial bladder cancer. Programmed cell death protein-1 (PD-1), cytotoxic T-lymphocyte-associated antigen 4 (CTLA4), and transforming growth factor-beta (TGF-β) are some of the examples of immune suppressors/checkpoints. They are responsible for deactivating the immune system and enhancing immunological tolerance. Moreover, they categorically downregulate and suppress the immune system by preventing and blocking the activation of T-cells, which in turn decreases autoimmunity and enhances self-tolerance. In cancer immunotherapy, the immune checkpoints/suppressors prevent and block the immune cells from attacking, spreading, and killing the cancer cells, which leads to cancer growth and development. We formulate a mathematical model that studies three possible dynamics of the treatment and establish the effects of the immune checkpoints on the immune system and the treatment at large. Although the effect cannot be seen explicitly in the analysis of the model, we show it by numerical simulations.

Introduction: Early detection is a cornerstone of cancer control, yet its quantitative influence on tumor–immune interactions remains underexplored in mathematical oncology.Methods: We formulated a nonlinear tumor–immune interaction model consisting of two coupled ordinary differential equations for tumor growth and immune response. Early detection was represented by a saturating function (Michealis-Menten term) dependent on tumor size and awareness level. The system was nondimensionalized to reduce parameters and ease analysis. Equilibria were derived, and both local and global stability were analyzed. Numerical simulations, phase portraits, bifurcation and sensitivity analyses were conducted to assess system behavior and parameter influence.Results: Two biologically meaningful equilibria were identified. Stability analyses established the conditions for sustained tumor-free states. Simulations demonstrated that higher awareness significantly enhances early detection, thereby suppressing tumor growth. Phase portraits revealed stable tumor–immune dynamics, while sensitivity results highlighted awareness- and detection-related parameters as the most critical for tumor control.Discussion: The model quantifies the role of awareness-driven early detection in shaping tumor–immune outcomes. Results underscore the importance of public awareness campaigns, screening initiatives, and early intervention strategies for effective cancer management. This framework bridges mathematical modeling and policy, offering understanding into optimizing awareness-based control measures.