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In this paper, we investigate a mathematical model of pancreatic cancer, which extends the existing pancreatic cancer models with regulatory T cells (Tregs) and Treg inhibitory therapy. The model consists of tumor-immune interaction and immune suppression from Tregs. In the absence of treatments, we first characterize the system dynamics by locating equilibrium points and determining stability properties. Next, cytokine induced killer (CIK) immunotherapy is incorporated. Numerical simulations of prognostic results illustrate that the median overall survival associated with treatment can be prolonged approximately from 7 to 13 months, which is consistent with the clinical data. Furthermore, we consider cyclophosphamide (CTX) therapy as well as the combined therapy with CIK and CTX. Intensive simulation results suggest that both CTX therapy and the combined CIK/CTX therapy can reduce the number of Tregs and increase the overall survival (OS), but Tregs and tumor cells will gradually rise to equilibrium state as long as therapies are ceased. [ABSTRACT FROM AUTHOR]

We consider a mathematical model that describes a viral infection with lytic and non-lytic immune responses. One of the main features of the model is that it includes a rate of linear activation of cytotoxic T lymphocytes (CTLs) immune response, a constant production rate of CTLs export from thymus, and a nonlinear attack rate for each immune effector mechanism. Stability of the infection-free equilibrium, and existence, uniqueness and stability of an immune-controlled equilibrium, are investigated. The stability results are given in terms of the basic reproductive number. We use the method of Lyapunov functions to study the global stability of the infection-free equilibrium and the immune-controlled equilibrium. We give a sufficient condition on the non-lytic-immune attack rate for the global asymptotic stability of the immune-controlled equilibrium. By theoretical analysis and numerical simulations, we show that the lytic and non-lytic activities are required to combat a viral infection. [ABSTRACT FROM AUTHOR]