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A mathematical model for the quantitative analysis of the interaction between cancer cells and cell-mediated immune system with two discrete-time delays, considering the role of antibodies, is studied in this paper. The model is analyzed both analytically and numerically to understand the dynamics of interaction delay and proliferation enhancement effect delay in the eradication of cancer. Hopf bifurcation occurs when one-time delay crosses the critical value in the absence of the other. It is also observed that as we increase any of the delays, it will increase the cancer burden. The analysis shows that a cancer-free state cannot be obtained solely by the killing rate of cytotoxic T-lymphocytes, but humoral response in combination with cell-mediated immune responses plays an important role to eradicate cancer. [ABSTRACT FROM AUTHOR]

In this paper, the schooling behavior of prey fish population in a predator–prey interaction is investigated. By taking an economical interest which can be elaborated by the presence of nonselective harvesting into consideration, we studied the dynamical behavior. The existence, positivity and boundedness of solution have been established. The analysis of the equilibrium states is presented by studying the local and the global stability. The possible types of local bifurcation that the system can undergoes are discussed. The effect of fishing effort on the evolution of the species is examined. Further, by using Pontryagin's maximum principle a proper management strategy has been used for avoiding the extinction of the considered species and maximizing the benefits. For the validation of the theoretical result, several of graphical representations have been used. [ABSTRACT FROM AUTHOR]

In this paper, a delayed differential model based on the intravenous glucose tolerance test is considered. The conditions to determine stability or instability of the model's steady state are obtained. We obtain the necessary conditions for the appearance of a bifurcation, and we investigate the direction and stability of the local bifurcation. For this purpose, the normal form theory is used. In addition, the numerical diagrams in the direction of theoretical results are drawn. [ABSTRACT FROM AUTHOR]