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Background: Food tax-subsidy policies are proposed to hold promise for helping to produce healthier patterns of food purchasing and consumption at population level. Evidence for their effects derives largely from simulation studies that explore the potential effects of untried policies using a mathematical modelling framework. This paper provides a critique first of the nature of the evidence derived from such simulation studies, and second of the challenges of cumulating that evidence to inform public health policy. Discussion: Effects estimated by simulation studies of food taxes and subsidies can be expected to diverge in potentially important ways from those that would accrue in practice because these models are simplified, typically static, representations of complex adaptive systems. The level of confidence that can be placed in modelled estimates of effects is correspondingly low, and the level of associated uncertainty is high. Moreover, evidence from food tax-subsidy simulation studies cannot meaningfully be cumulated using currently available quantitative evidence synthesis methods, to reduce uncertainty about effects. Summary: Simulation studies are critical for the initial phases of an incremental research process, for drawing together diverse evidence and exploring potential longer-term effects. While simulation studies of food taxes and subsidies provide a valuable and necessary input to the formulation of public health policy in this area, they are unlikely to be sufficient, and policy makers should not place excessive reliance on evidence from such studies, either singly or cumulatively. To reflect known and unknown limitations of the models, results of such studies should be interpreted cautiously as tentative projections. Modelling studies should increasingly be integrated with more empirical studies of the effects of food tax and subsidy policies in practice. [ABSTRACT FROM AUTHOR]

Background: The haematopoietic lineages with leukaemia lineages are considered in this paper. In particular, we mainly consider that haematopoietic lineages are tightly controlled by negative feedback inhibition of end-product. Actually, leukemia has been found 100 years ago. Up to now, the exact mechanism is still unknown, and many factors are thought to be associated with the pathogenesis of leukemia. Nevertheless, it is very necessary to continue the profound study of the pathogenesis of leukemia. Here, we propose a new mathematical model which include some negative feedback inhibition from the terminally differentiated cells of haematopoietic lineages to the haematopoietic stem cells and haematopoietic progenitor cells in order to describe the regulatory mechanisms mentioned above by a set of ordinary differential equations. Afterwards, we carried out detailed dynamical bifurcation analysis of the model, and obtained some meaningful results. Results: In this work, we mainly perform the analysis of the mathematic model by bifurcation theory and numerical simulations. We have not only incorporated some new negative feedback mechanisms to the existing model, but also constructed our own model by using the modeling method of stem cell theory with probability method. Through a series of qualitative analysis and numerical simulations, we obtain that the weak negative feedback for differentiation probability is conducive to the cure of leukemia. However, with the strengthening of negative feedback, leukemia will be more difficult to be cured, and even induce death. In contrast, strong negative feedback for differentiation rate of progenitor cells can promote healthy haematopoiesis and suppress leukaemia. Conclusions: These results demonstrate that healthy progenitor cells are bestowed a competitive advantage over leukaemia stem cells. Weak g1, g2, and h1 enable the system stays in the healthy state. However, strong h2 can promote healthy haematopoiesis and suppress leukaemia. [ABSTRACT FROM AUTHOR]