Search

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]

In this paper, we introduce ordinary and delay differential equations to describe the interactions between a malignant tumour and the immune systemin vivoin the presence of human immunodeficiency virus (HIV) infection of CD4+T-cells. In the delay model, we take into account the time lags required by the healthy effector cell components to recognize the pathogens and tumour cells. The models consist of four populations: tumour cells, healthy effector cells (CD4+T-cells), effector cells infected by HIVs and free viral particles. The presence of delay term in the model leads to a notable increase in the complexity of the observed behaviour. We investigate the qualitative behaviour of the models and find the conditions that guarantee the asymptotic stability of the steady states. Numerical simulations are provided to illustrate and extend the theoretical results. The obtained results are consistent with the real phenomena and give a better understanding of cancer immunity and viral oncogenesis. [ABSTRACT FROM PUBLISHER]