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In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $$d_2$$ d 2 -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.

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INTRODUCTION:Hospital care transformation plan (HCTP) was implemented, in 2014, with the aim of ensuring all Iranians have fair access to hospital care, mainly in the public sector. It was assumed that HCTP would lead to increased quality and effectiveness of health care in public hospitals. To explore whether HCTP has achieved its aim, this study has investigated the impact of this plan on performance indicators (PIs) of the public hospitals.MATERIALS AND METHODS:This cross-sectional descriptive study was conducted in 2016. The study population included all hospitals in the Isfahan City. Data (10 selected PIs) were collected through formal reports which were available at the Isfahan University of Medical Sciences and analyzed using Statistical Package for Social Sciences (version 17). The statistical significant level analysis was 0.05.RESULTS:After HCTP, it was shown an increase of (1) Bed occupancy, bed turnover, occupied bed-days, inpatients visits, and number of surgeries in all types of hospitals, (2) Outpatients’ visits in all hospitals except private ones, (3) Emergency visits in public and social security hospitals, and (4) Natural deliveries in public and semi-public hospitals. Furthermore, the average length of stay and hospital mortality rate has decreased in all types of hospitals after HCTP implementation.DISCUSSION AND CONCLUSION:Although, improving PIs of hospitals were not directly stated and known objectives of HCTP implementation, it seems HCTP could improve the performance of all hospitals, including involved and noninvolved ones.

In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $d_2$-distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process.

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In this work we consider the mean-field traveling salesman problem, where the intercity distances are taken to be independent and identically distributed with some distribution F. We consider the simplest approximation algorithm, namely, the nearest-neighbor algorithm, where the rule is to move to the nearest nonvisited city. We show that the limiting behavior of the total length of the nearest-neighbor tour depends on the scaling properties of the density of F at 0 and derive the limits for all possible cases of general F.