| Objective:1.Describe the changes and current situation of medical and health resource allocation in Changchun City from 2012 to 2019,and analyze possible problems in the allocation of medical and health resources;2.Explore new allocation standards for medical and health resources,construct mathematical models for optimal allocation of limited medical and health resources,and provide important model tools and decision-making references for Health Commission of Changchun City.Methods:Part 1 data were sourced from the "Changchun Municipal Health and Health Commission Direct Reporting System and Collection of Health Statistics" to obtain data on the number of medical institutions,the number of beds in medical institutions,the number of health personnel,and the number of hospital admissions during the period 2012-2019.Excel 2010 was used to collate the data,and SPSS 19.0 software was used to calculate the absolute number,component ratio,average annual growth rate,year-on-year growth rate,annual utilization rate,and other indicators to describe the current situation of medical and health resource allocation in Changchun City.Part 2 data were sourced from CNKI,Chinese Medical Literature Database,and case data from the First Hospital of Jilin University in 2019 to obtain data on patient size,intrinsic utility,value-added utility,treatment costs,and other data in the case.The social welfare function in welfare economics and the ideal point method in multi-objective optimization were used to construct a new allocation standard for medical and health resources.The optimization method in mathematical modeling were used to construct a mathematical model for the optimal allocation of medical and health resources.The Yalmip toolbox loaded by Matlab software was used to solve the model and preliminary application.Results:1.Allocation of medical and health resources in Changchun City from 2012 to 2019.1.1 The total number of medical and health institutions increased from 3987 in 2012 to 4918 in 2019,with an average annual growth rate of 3.04%.The year with the largest year-on-year growth was 2018(17.28%).The number of hospitals,primary medical and health institutions,and professional public health agencies increased from 167 to 188,3768 to 4612,and 48 to 114,with average annual growth rates of 1.71%,2.91%,and 13.15%,respectively.During the past seven years,the absolute number of hospitals,primary medical and health institutions,and professional public health agencies had all increased,but the number of township health centers and village clinic in primary medical and health institutions has continuously decreased,with an average annual decline of 1.59% and0.43%,respectively.In 2019,Changchun had 6.53 medical and health institutions per10000 people.The number of hospitals,primary medical and health institutions,and professional public health agencies per 10000 people in Changchun is 0.25,6.12,and 0.15,respectively.1.2 The total number of health personnel increased from 59158 people in 2012 to76216 people in 2019,with an average annual growth rate of 3.68%.The number of health technical personnel increased from 42934 to 58587 people,with an average annual growth rate of 4.54%.The number of rural doctors and health workers decreased from 6313 to4375 people,with an average annual decline of 5.10%.In 2018,both the year-on-year growth of the total amount and the year-on-year growth of health technical personnel reached the maximum(9.93% and 13.83%),while the year-on-year decline of rural doctors and health workers was the largest(12.4%)in the same year.In the past seven years,the total number of health personnel has continued to grow,with a net increase of 17058 people,the number of health technical personnel has increased year by year,with a net increase of 15653 people.However,the number of rural doctors and health workers continued to decrease,with a net decrease of 1938 people.In 2019,Changchun had 10.11 health personnel per 1000 people.The number of health technical personnel,licensed(assistant)doctors,and registered nurses per 1000 people was 7.77,3.35,and 3.33,respectively.The ratio of doctor and nurse in Changchun was 1:0.99.1.3 The number of beds in medical and health institutions increased from 42283 in2012 to 56348 in 2019,with an average annual growth rate of 4.18%.The largest year-on-year increase was in 2018(6.61%).The number of hospital beds increased from36582 to 51139,with an annual growth rate of 4.90%.The number of beds in primary medical and health institutions increased from 4329 to 4436,with an annual growth rate of0.35%.The number of beds in professional public health agencies decreased from 707 to632,with an average annual decline of 1.59%.In 2019,Changchun City had 7.48 beds per1000 people,including 6.78 hospital beds and 4.33 general hospital beds per 1000 people.1.4 The total number of hospitals at all levels increased from 71 in 2012 to 109 in2019,with an average annual growth rate of 6.32%,showing an overall increasing trend.The average annual growth rate of first-level and secondary hospitals(5.96%,7.93%)was higher than that of tertiary hospitals(3.09%).By the end of 2019,there were 21 tertiary hospitals,58 secondary hospitals,and 30 first-level hospitals,respectively.In terms of the average annual utilization rate of hospital beds,tertiary hospitals were the highest(97.5%),followed by secondary hospitals(78.1%),and first-level hospitals were the lowest(27.1%).2.Allocation standards and optimization models of medical and health resources.2.1 Based on utilitarian and fairness standard,we had established three weighted allocation standards for the allocation of medical and health resources.The weighted utilitarianism standard was to select individual weight coefficients based on actual situations to maximize the overall utility level of all members after weighting.The weighted fairness standard was that the allocation scheme of medical and health resources should maximize the utility of individuals with relatively low utility levels among the weighted member.The weighted ideal point standard was to make the allocation scheme of medical and health resources closest to the ideal state.2.2 Based on the social welfare function,health equity theory,and optimization methods,and taking the utility level of each individual as the optimization goal,a multi-objective optimization model and a group multi-objective optimization model were constructed for the allocation of limited medical and health resources.Under the weighted utilitarianism standard,weighted fairness standard and weighted ideal point standard,the optimization models and group optimization models of limited medical and health resources allocation were constructed.2.3 Taking two simple cases of individuals as patient groups,the optimization model and the extended model under the weighted utilitarianism standard were initially applied.When the weight coefficients of most individuals are close,the utilitarian standard will play a leading role,i.e.efficiency is dominant.Common diseases(or mild diabetes)can receive budget fund allocation by hospitals at all levels,while severe diseases(or severe diabetes)receive budget fund allocation reduction by hospitals at all levels.When the weight coefficient take the larger value for severe diseases(or severe diabetes)with low utility values,the allocation of budget funds by hospitals at all levels are tilted towards severe diseases(or severe diabetes).At this time,the allocation scheme is dominated by fairness standards,i.e.fairness is dominant.According to the specific situation,by adding constraint modules and adjusting the weight coefficient,we can ensure that patients with common diseases(or mild diabetes)are treated by hospitals,and patients with severe diseases(or severe diabetes)are treated by tertiary hospitals,so that the budget fund allocation plans of hospitals at all levels focus on fairness while taking into account efficiency.Conclusions:1.The allocation of the number of medical and health institutions in Changchun City had continuously improved,and the total number of health personnel had steadily increased,but the growth rate between urban and rural areas was uneven.Moreover,rural doctors and health workers were decreasing year by year,and the problem of insufficient nurses remains serious.It is suggested that the government health department can increase the investment in rural health human resources according to the actual situation,and increase the training and introduction of nursing talents.It is recommended to appropriately increase the number of beds in primary medical and health institutions,increase the utilization rate of beds in medical institutions below the second level,and reduce the pressure on inpatient beds in tertiary hospitals.2.Under the weighted allocation standards of utilitarianism,fairness,and ideal point,the multi-objective optimization models and the group optimization models for the optimal allocation of medical and health resources were constructed,with the individual utility level as the optimization goal.Case analysis shows that the model has good promotion and expansion value,and is not only suitable for the allocation of medical resources among hospitals at all levels,but also for the optimal allocation of medical and health resources among urban medical and health institutions. |
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