An alternative delayed population growth difference equation model

Continuous quality improvement project to reduce the downtime of medical linear accelerators: A case study at Zhejiang Cancer Hospital

Objective

To analyse and continually improve existing issues in the quality improvement process of medical linear accelerators (LINACs) and enhance the quality control management of LINACs.

Methods

Data were collected from eight LINACs (sourced from three manufacturers) at Zhejiang Cancer Hospital using Excel diaries between January 2019 and December 2020. The data description and analysis were performed using the analytic hierarchy process, SPSSAU and Excel software, and mean-time-to-repair (MTTR)/mean-time-between-failure (MTBF) metrics. Continuous quality improvement was executed using the quality control circle (QCC) quality management method.

Results

After quality improvement, the risk frequency of 'LINAC down' events decreased by 43.63% and downtime was reduced by 40.45%. The weight of downtime risk improved by 73.69%. The MTTR recovery value increased by 31.90%, and MTBF reliability increased by 2.97 h. The simulation results demonstrated that the proposed quality improvement measures could effectively decrease the frequency and duration of downtimes, consequently extending the normal operational time of LINACs.

Conclusion

Transitioning from instant repair to preventative maintenance can enhance the operational efficiency of equipment and yield economic benefits for hospitals. The QCC method and the event risk evaluation model are effective in reducing the downtime of LINACs and improving their quality control management.

Technique to derive discrete population models with delayed growth

We provide a procedure for deriving discrete population models for the size of the adult population at the beginning of each breeding cycle and assume only adult individuals reproduce. This derivation technique includes delay to account for the number of breeding cycles that a newborn individual remains immature and does not contribute to reproduction. These models include a survival probability (during the delay period) for the immature individuals, since these individuals have to survive to reach maturity and become members of, what we consider, the adult population. We discuss properties of this class of discrete delay population models and show that there is a critical delay threshold. The population goes extinct if the delay exceeds this threshold. We apply this derivation procedure to obtain two models, a Beverton-Holt adult model and a Ricker adult model and discuss the global dynamics of both models.

Population growth and competition models with decay and competition consistent delay

We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in the growth term is consistent with the rate of instantaneous decline in the population given by the model. Our formulation is a modification of Arino et al. (J Theor Biol 241(1):109-119, 2006) by taking the intraspecific competition between the adults and juveniles into account. We provide a complete global analysis showing that no sustained oscillations are possible. A threshold giving the interface between extinction and survival is determined in terms of the parameters in the model. The theory of chain transitive sets and the comparison theorem for cooperative delay differential equations are used to determine the global dynamics of the model. We extend our delayed logistic equation to a system modeling the competition between two species. For the competition model, we provide results on local stability, bifurcation diagrams, and adaptive dynamics. Assuming that the species with shorter delay produces fewer offspring at a time than the species with longer delay, we show that there is a critical value, [Formula: see text], such that the evolutionary trend is for the delay to approach [Formula: see text].