A mathematical model of Public-Private Partnership in Medical Alliance of
医学联盟公私合作 的数学模型
Chinese Health Care
中国保健
Abstract
抽象
China has carried out a new round of medical reform. Medical Alliance (MA) which integrates medical resources in the same area is becoming a popular model in the medical reforms. Although MAs have been carried out nationwide for a few years，a series of problems have emerged during the practice. A public-private partnership (PPP) is a cooperative arrangement between two or more public and private sectors and lots of countries are increasingly looking to the PPP-model to solve larger problems in healthcare. In this study, by matrix mathematical model calculation and data from China’s Health Statistical Yearbook, the author analyzes the necessity and feasibility of the wide application of MA in the PPP model in China basic health care. After the “The Basic Health and Health Promotion Law” in 2020, PPP model can be applied in Medical Alliance of Chinese health care but remain lots of challenges.
中国开展了新一轮医疗改革。整合同一领域医疗资源的医学联盟（MA）正在成为医疗改革的流行模式。虽然 MA 在全国范围内开展了几年，但在实践过程中出现了一系列问题。公私伙伴关系 （PPP） 是两个或多个公共和私营部门之间的合作安排，许多国家越来越多地寻求 PPP 模式来解决医疗保健领域的更大问题。本文通过矩阵数学模型计算和《中国卫生统计年鉴》数据，分析了 MA 在 PPP 模型中广泛应用在中国基础卫生保健中的必要性和可行性。2020 年《基本健康与健康促进法》出台后，PPP 模式在中国健康医疗联盟中得到应用，但仍面临诸多挑战。
Key Words: Public-Private Partnership; Medical Alliance; Medical Service; China Medical Reform
关键词： 公私伙伴关系;医学联盟;医疗服务;中国医改
1. Introduction
1. 简介
China carried out a new round of medical reform form 2009. Ever since then, Chinese Health Care service have effectively improved. However, there are still lots of problems in China's basic health care, especially in Chinese Health Care. It is the rigid pattern of administrative ideas and irrational allocation of medical resources that brings difficulties to medical care in China. In terms of Chinese Health Care , hardware facilities are insufficient, as well as capital investment. many historical debts, incomplete personnel distribution and heavy historical burden are present during the reform, which restrict the development of Chinese Health Care.
2009年，中国开展了新一轮医改改革。从那时起，中国医疗保健服务得到了有效的改善。然而，我国的基本卫生保健，尤其是中国卫生保健，仍然存在很多问题。正是行政思想的僵化格局和医疗资源配置的不合理给我国的医疗带来了困难。在中国医疗方面，硬件设施不足，以及资金投入。改革期间存在许多历史债务、人员配置不全和沉重的历史负担，制约了中国医疗事业的发展。
Many fundamental problems occur in the development of health care and need to be standardized by basic and comprehensive laws. At the same time, the practices which have proved to be effective and specific systems which work well in the clinic should also be incorporated into law. In 2018, the Thirty-first Meeting of the Twelve NPC Standing Committees of China reviewed the first draft of “The Basic Health and Health Promotion Law”. The formulation of such law provides for the possibility of a standard for the nature of health services and the basic health system, the right of citizens' to healthcare and healthcare investment of the government. With the help of this law, governmental healthcare investment can be optimized, and the imbalance between supply and demand of medical services can be eased. In the first draft of “The Basic Health and Health Promotion Law”, private investors were encouraged to have input on medical and health institutions. The draft only included the layout for public health institutions to meet the requirements of planning. It does not restrict medical institutions organized by private investments. At the same time, it emphasizes the importance of public hospitals. The development of public hospitals will be more public benefit oriented.
卫生保健事业发展中存在许多根本性问题，需要通过基本和综合性法律来规范。同时，已被证明是有效的做法和在临床上行之有效的具体系统也应纳入法律。2018年，中国十二届全国人大常委会第三十一次会议审议了《基本健康与健康促进法》初稿。这种法律的制定规定了为保健服务的性质和基本保健系统、公民的保健权和政府的保健投资制定标准的可能性。借助该法律，可以优化政府医疗投资，缓解医疗服务供需失衡。在《基本健康与健康促进法》初稿中，鼓励民间投资者对医疗卫生机构提出意见。草案仅纳入了公共卫生机构符合规划要求的布局。它不限制民间投资组织的医疗机构。同时，它强调了公立医院的重要性。公立医院的发展将更加以公益为导向。
Medical Alliance (MA) is a regional medical consortium that integrates medical resources in the same area. It is a new measure which was proposed to solve the problem of“Difficulty and Expensiveness of Medical Service”. It usually consists of a tertiary Hospital in a region, a secondary hospital, a community/ village hospital. This MA model is rising in China. MA is considered to be helpful to solve the problems of irrational allocation of medical and health resources, as well as insufficient government investment and inefficient public hospitals. It has become a useful endeavor to alleviate the shortage of medical resources, improve the accessibility of medical services and meet the diversified needs of medical services. In the field of Chinese Health Care. MA is also considered to be effective in improving the capacities of Chinese Health Care.
医学联盟（MA）是一个整合同一地区医疗资源的区域性医疗联合体。这是为解决“医疗服务难度大、医疗费用高”问题而提出的一项新措施。它通常由一个地区的三级医院、二级医院、社区/乡村医院组成。这种 MA 模式在中国正在兴起。MA 被认为有助于解决医疗卫生资源配置不合理、政府投入不足、公立医院效率低下等问题。它已成为缓解医疗资源短缺、提高医疗服务可及性、满足医疗服务多样化需求的有益努力。在中国医疗保健领域。MA 也被认为可以有效提高中国医疗保健的能力。
Although MAs have been carried out nationwide for a few years，a series of problems have emerged during the practice，and now the policy is in a dilemma. As an important part of leading the new pattern of health reform, the ultimate goal of MA should have been the subsidence of medical resources and finance to the community. However, statistic data showed that, in the year 2017, 70% of the health costs were concentrated in the hospital, and more than half were in the tertiary Hospital/institutions; the community/village hospital accounted for only about 15%, and the pharmacy and other institutions accounted for about 8%, showing a clear inverted triangle model, which is no good to MA. Therefore, exploring the sources of the problems，finding a suitable model of PPP in Chines MA and putting forward relevant strategies are key points in ensuring the healthy and sustainable development of the Health Alliance Policy.
虽然 MA 在全国范围内开展了几年，但在实践过程中出现了一系列问题，现在政策陷入了两难境地。作为引领医疗改革新格局的重要一环，MA 的最终目标本应是医疗资源和财政下沉社会。但统计数据显示，2017 年，70%的医疗费用集中在医院，超过一半在三级医院/机构;社区/村医院仅占 15%左右，药房等机构占比 8%左右，呈现明显的倒三角模式，对 MA 不利。因此，探究问题根源， 寻找适合中国 MA 的 PPP 模式并提出相关策略，是保障健康联盟政策健康可持续发展的关键点。
A public-private partnership (PPP) is a cooperative arrangement between two or more public and private sectors, which can be applied in lots of areas, (1), typically of a long-term nature. PPP has been used to finance health and medical initiatives (2, 3). Lots of countries are increasingly looking to the PPP-model to solve larger problems in healthcare (4-10). Generally speaking, only the hospital is the only medical infrastructure that is large enough to attract the private sector (11). Nowadays, private capital and expertise have increasingly become the sources of increased efficiency and innovation(12), and PPP is an opportunity to reduce the overall cost of healthcare. Herein, by matrix mathematical model calculation and data from China’s Health Statistical Yearbook, the author analyzes the necessity and feasibility of the wide application of MA in the PPP model after the “The Basic Health and Health Promotion Law” in 2020.
公私伙伴关系 （PPP） 是两个或多个公共和私营部门之间的合作安排，可以应用于许多领域，（1），通常具有长期性质。PPP 已被用于资助健康和医疗计划 （2， 3）。许多国家越来越多地寻求 PPP 模式来解决医疗保健领域的更大问题 （4-10）。一般来说，只有医院是唯一足够大以吸引私营部门的医疗基础设施 （11）。如今，私人资本和专业知识日益成为提高效率和创新的源泉（12），而 PPP 是降低医疗保健总体成本的机会。本文通过矩阵数学模型计算和《中国卫生统计年鉴》数据，分析了 2020 年《健康与健康促进基本法》颁布后，MA 在 PPP 模型中广泛应用的必要性和可行性。
Methods
方法
In order to find out the relationship between MA and the increasing of private health sectors in Mainland China, the authors identified key information from government official websites as well as data from China’s Health Statistical Yearbook. This work was supported by top-notch innovative talents project of Fujian （Fujian Provincial Committee Office 2016 -11 &2021J01782） Fujian Medical University teaching reform project (Y17005) and Fujian Provincial Health Commission Youth Research Project（2021GCA018）This study protocol was approved by ethics review committee of Institute of China Free Trade Zone Law, East China of Political Science and Law
为了了解 MA 与中国大陆私营卫生部门增加之间的关系，作者从政府官方网站以及中国卫生统计年鉴中确定了关键信息。福建省拔尖创新人才项目（ 福建省委办公室，2016-11 &2021J01782）、福建医科大学教学改革项目（Y17005）、福建省卫健委青年科研项目（2021GCA018）支持 ，经中国自由贸易区法学研究院华东政法研究所伦理审查委员会批准
Results:
结果：
1. the necessity of the wide application of MA in PPP model
1. MA 在 PPP 模式中广泛应用的必要性
The new healthcare reform has put forward the important task of accelerating the formation of a diversified medical service pattern, by introducing social capital to increase the supply of medical services. In 2017 March, China Premier Li Keqiang pointed out in the government work report that "we will perform a pilot test of diversified forms and models of MA", which means the application of MA will emerge in large numbers. It is the inevitable choice to solve the plight of basic medical services in China. In practical operation, private hospitals find it difficult to truly develop and grow due to various reasons, while public hospitals face the problem of a moderate reduction in proportion due to their large size. As a result, mixed ownership hospitals (PPP projects) have emerged. Among those diversified forms and models of MA, the PPP model is a very promising one. The rigid pattern of administrative ideas and irrational allocation of medical resources created by the government have brought many difficulties to MA. Meanwhile, the wide application of MA in the PPP model in the basic medical field can better coordinate the role of the public and private sectors(13). In detail, the public sector is responsible for decision making, guiding private investment in the field of basic medical services, as well as providing incentives, supervision and coordination. The private sector can provide medical services in medical service infrastructure construction (such as hospital buildings, large medical devices), normal operation of hospitals (such as property management) and specialized medical services, etc., which is a way of integrating MA in the PPP model.
新医改提出了加快形成多元化医疗服务格局的重要任务，通过引入社会资本增加医疗服务供给。2017 年 3 月，中国总理李克强在政府工作报告中指出，“我们将对 MA 进行多样化形式和模式的试点测试”，这意味着 MA 的应用将大量涌现。是解决我国基础医疗服务困境的必然选择。 在实际作中，民营医院由于种种原因难以真正发展壮大，而公立医院则因规模较大，面临比例适度下降的问题。因此，出现了混合所有制医院（PPP 项目）。 在 MA 的多元化形式和模式中，PPP 模式是一个非常有前景的模式。政府制造的僵化的行政思想格局和医疗资源的不合理配置给马术学院带来了诸多困难。同时，MA 在基础医学领域 PPP 模式的广泛应用可以更好地协调公私部门的作用（13）。具体来说，公共部门负责决策，指导基本医疗服务领域的民间投资，以及提供激励、监督和协调。民营部门可以在医疗服务基础设施建设（如医院建筑、大型医疗器械）、医院正常运营（如物业管理）和专科医疗服务等方面提供医疗服务，是将 MA 融入 PPP 模式的一种方式。
Competitive neutrality means public (state-owned) and private businesses compete on the same level, which is essential for the effective use of medical resources. Thus, It encourages healthy growth and development. The principle of competitive neutrality is gaining worldwide support; however, obtaining it in China in practice is a difficult question.Public hospitals are limited by various personnel, financial, material, and investment management systems and cannot develop according to their own plans. Private capital with funds cannot compete with public hospitals for talent resources due to personnel and career development restrictions. The wide application of MA can break the limitation of monopoly public investment of the hospital. After the elimination of the monopoly in the basic medical field by the wide application of MA, a more orderly and healthy competition environment can be built. The wide application of MA, to a certain extent, can promote the establishment of competitive neutrality, which is of great importance for China. (14)At present, from the perspective of social capital, private medical institutions still face policy barriers in various aspects such as admission, planning, staffing, professional titles, scientific research, pricing, and medical insurance. Adopting the PPP medical institution approach is aimed at obtaining support from government regulatory authorities and reducing policy discrimination; On the other hand, private sectors also want to leverage the existing brands, technologies, and talents of public hospitals to accelerate development.
竞争中立意味着公共（国有）和私营企业在同一水平上竞争，这对于有效利用医疗资源至关重要。因此，它鼓励健康的成长和发展。竞争中立原则正在获得全世界的支持;然而，在实践中在中国获得它是一个困难的问题。 公立医院受制于各种人员、财务、物资、投资管理制度，无法按照自己的规划发展。有资金的民间资本，由于人员和职业发展的限制，无法与公立医院争夺人才资源。 MA 的广泛应用可以打破医院垄断公共投资的限制。通过 MA 的广泛应用消除基础医学领域的垄断后，可以构建更加有序、健康的竞争环境。MA 的广泛应用，一定程度上可以促进竞争中立的建立，这对中国来说具有重要意义。（14） 目前，从社会资本来看，民营医疗机构在招生、规划、人员配备、职称、科研、定价、医保等多方面仍面临政策壁垒。采用 PPP 医疗机构方式，旨在获得政府监管部门的支持，减少政策歧视;另一方面， 民间也希望利用公立医院现有的品牌、技术和人才来加速发展。
Theoretically, The wide application of MA can improve the current basic medical services in China. It will ease the financial pressure on the government and increase the supply of basic medical service resources. It will also relieve the contradiction between the basic medical supply and the patient demand; on the other hand, the wide application of MA in the PPP model can change the mode of bureaucracy in public sectors and promote the optimal allocation of resources. In addition, with the help of professional management knowledge and experience in the private sector, MA can provide better medical services for the public using professional and modern medical technology. Through the PPP mode, people can also introduce the market-oriented approach, establish a market-oriented management/ performance evaluation system, improve the operation efficiency of MA, and maximize the utilization value of funds through risk sharing between the public and private sectors. However, is it true in real world practice?
从理论上讲，MA 的广泛应用可以改善我国当前的基础医疗服务。缓解政府财政压力，增加基本医疗服务资源供给。也将缓解基本医疗供给与患者需求的矛盾;另一方面，MA 在 PPP 模式中的广泛应用可以改变公共部门的官僚主义模式，促进资源的优化配置。此外，借助专业的管理知识和私营部门的经验，MA 可以利用专业和现代医疗技术为公众提供更好的医疗服务。通过 PPP 模式，人们还可以引入市场化的方式，建立市场化的管理/绩效评估体系，提高 MA 的运行效率，通过公私部门的风险分担，实现资金的利用价值最大化。 然而，在现实世界的实践中是真的吗？
2.matrix mathematical model calculation
2. 矩阵数学模型计算
One of the major concerns about the wide application of MA in PPP model is the trust issue between the government and the public/private sectors. We use a model in the field of MA (Table 1). The basic income obtained by the government from MA is “Z”. The basic income obtained by the MA is “Q”; if the public/private sectors in the MA are actively cooperating, both sectors can obtain incentive income “R”. If the sectors in the MA are negatively cooperating, and they may be punished by the government for a certain amount of “P”, however, they might obtain additional benefits “E” from the “negative cooperating”. For the government to obey the contract of supporting MA, it will also increase the social cost “S”. If the government breaks the contract, it will reduce the support “W” to MA, but the government regulators will punish the government “B”. If the government breaks the contract of supporting MA and the sectors in the MA are negatively cooperating, it will eventually hurt the public, and their interests will not be guaranteed. The MA will reduce its profits by “C”. The probability of the government to obey the contract of supporting MA is “x”. The probability of breaking the contract is “1 – x”, and the probability of actively cooperating by the MA is “y”. The probability of negatively cooperating by the MA is “1 – y”
MA 在 PPP 模式中的广泛应用的主要担忧之一是政府与公共/私营部门之间的信任问题。我们在 MA 领域使用了一个模型（表 1）。政府从 MA 获得的基本收入为“Z”。MA 获得的基本收入为“Q”;如果 MA 中的公共/私营部门积极合作，两个部门都可以获得激励收入“R”。如果 MA 中的部门是负面合作的，并且可能会因一定数量的“P”而受到政府的惩罚，但是，它们可能会从“负面合作”中获得额外的利益“E”。对于政府来说，服从支持 MA 的契约，也会增加社会成本“S”。如果政府违约，将减少对 MA 的支持“W”，但政府监管机构将惩罚政府“B”。如果政府违背支持马的契约，马内各界进行消极合作，最终会伤害到公众，他们的利益得不到保障。金融管理平台将减少其利润“C”。政府遵守支持 MA 契约的概率为“x”。违约概率为“1 – x”，MA 主动配合的概率为“y”。MA 负向合作的概率为“1 – y”
In the matrix,when government obeys the MA contract, the benefit expectation Ego=(Z- R)y+(Z- E+P- S)(1- y); when government breaks the contract, the Benefit expectation Egb=(Z- R+W- B)y+(Z+W- E+P- B)(1- y).
在矩阵中，当政府遵守 MA 契约时，收益期望值 Ego=（Z-R）y+（Z-E+P-S）（1-y）;当政府违约时，收益期望值 Egb=（Z- R+W- B）y+（Z+W- E+P- B）（1- y）。
Then the dynamical equation for the government is as follows
那么政府的动态方程如下
F(x)= dX/dt=x(1- x)(Sy+B-W-S) ①
F（x）= dX/dt=x（1- x）（Sy+B-W-S） （1）
In the matrix,when MA actively cooperates, the benefit expectation Ema=(Q+R)x+(Q+R-W)(1- x)=Wx+Q+R-W; when MA negatively cooperates, the benefit expectation Emn=(Q+E- P)x+(Q+E- P-W- C)(1- x)=Cx+Wx+E+Q- C-P-W
矩阵中，当 MA 主动配合时，收益预期 Ema=（Q+R）x+（Q+R-W）（1- x）=Wx+Q+R-W;当 MA 负向配合时，收益期望 Emn=（Q+E- P）x+（Q+E- P-W- C）（1- x）=Cx+Wx+E+Q- C-P-W
Then the dynamical equation for the MA is as follows
那么 MA 的动力方程如下
F(y)= dY/dt= y(1- y)(C+P+R- E- Cx) ②
F（y）= dY/dt= y（1- y）（C+P+R- E- Cx） （2）
Equation (1) and Equation (2) form the Dynamical Systems
方程 （1） 和方程 （2） 构成动力系统
J= ③
J=（3）
The Jacobian matrix is as follows
雅可比矩阵如下
J= ④
J=（4）
According to mathematical model calculation, by the Hartman–Grobman theorem,(15),for the government, if W>B, the government is prone to break the MA contract; for MA, if E>P+R, the MA is prone to negatively cooperate.
根据数学模型计算，根据 Hartman-Grobman 定理 （15）， 对于政府来说，如果 W>B，政府容易破坏 MA 契约;对于 MA，如果 E>P+R，MA 容易发生负向合作。
If benefits of the government breaking the MA contract are far less than the cost of discrediting, and/or, the additional benefits of the MA negatively cooperating are far less than the incentive income of actively cooperating, both sides will choose "win-win strategy". In this case, the trust will be conducted along the good direction. In future cooperation, the MA will cooperate actively and the long-term cooperation to the government will be an identity trust, and this PPP will reduce the situation of renegotiation. And in this cooperative, all parties will take care of each other's benefits and trust transmission will go in a positive way.
如果政府破坏 MA 契约的收益远小于抹黑成本，和/或 MA 负面合作的额外收益远小于积极合作的激励收入，双方都会选择“双赢策略”。在这种情况下，信托将沿着良好的方向进行。在未来的合作中，MA 将积极合作，与政府的长期合作将是身份信托，本次 PPP 将减少重新谈判的情况。而在这个合作社中，各方都会照顾到彼此的利益，信任传递也会以积极的方式进行。
Verification of the matrix mathematical model calculation
矩阵数学模型计算的验证
China has launched a round of reform (Table 2).As is known to all, medical services are used to meet the health needs of the public. Basic medical care is an important part of medical services. It is based on the minimum medical need of the public. Within recent years, changes were introduced to contain costs and enable health-care resources in order to increase efficiency. Generally, all these have meant reduced public coverage and decreased publicly funded health services. In 2009, China initiated a new round of medical reform, and PPPs were encouraged to be applied to public medical care.
中国已经启动了一轮改革（表 2）。众所周知，医疗服务是用来满足公众的健康需求。基本医疗是医疗服务的重要组成部分。它基于公众的最低医疗需求。近年来，为了控制成本并启用医疗保健资源，引入了改革，以提高效率。 一般来说，所有这些都意味着公共覆盖面的减少和公共资助的卫生服务的减少。2009 年，中国启动新一轮医疗改革，鼓励 PPP 应用于公共医疗。
MA is a new measure which was proposed to solve the problem of“Difficulty and Costliness of Medical Services”.Before 2013 (MA was proposed), China had increasing private health sectors (Fig 1 A&B). As proposed in the government work report in 2017, various forms of MA should start to be put in place. The Office of State Council issued a "guide line on promoting the construction and development of MA", which integrates medical resources together in the same area. According to the guidelines, according to the will of the private institution, private investments can be integrated into MAs. Given the encouragement of the guidelines, private institutions can formulate the overall strategy of development according to the needs of their patients, and promote cooperation between public and private sectors. The wide application of MA in the PPP model can be win-win cooperation in regards to technical guidance, personnel training, and medical resource sharing and so on. This MA model can provide a wide range of medical services, meet the medical needs of people from different classes, and promote the rational allocation of medical resources in society.
MA 是为解决“医疗服务难度大、成本高”问题而提出的一项新措施。在 2013 年（提出 MA）之前，中国的私营卫生部门不断增加（图 1 A 和 B）。正如 2017 年政府工作报告所建议的那样，应开始实施各种形式的管理计划。国务院办公室印发《关于推进 MA 建设和发展的指导方针》，将医疗资源整合到同一区域。根据指导意见，根据民间机构的意愿，民间投资可以纳入 MA。在指引的鼓励下，民营机构可按病人需要制定整体发展策略，促进公私营部门合作。MA 在 PPP 模式中的广泛应用，可以在技术指导、人才培养、医疗资源共享等方面实现合作共赢。这种 MA 模式可以提供广泛的医疗服务，满足不同阶层人群的医疗需求，促进社会医疗资源的合理配置。
The “Ruijin Model” is a very important step in Chinese medical reform and a case that verified our matrix mathematical model calculation. Since proposed by the former health minister, Chen Zhu, in the national health conference in 2013, there have been more and more MAs in the country, with a variety of management and cooperation modes. One of the most successful cases is the “Ruijin Model”. In March 16, 2016, Shanghai Jiaotong University School of Medicine Ruijin Hospital (Ruijin hospital for Brief) together with other 8 hospitals in Shanghai, jointly set up “Ruijin Hematology MA”, it was the first hematology MA in Shanghai. It integrates and share medical resources and solves practical problems of patients with blood diseases. Ten years ago, it was also Ruijin hospital that founded the first medical union of Shanghai (Luwan District MA). In this MA, public sectors and the private sectors can both obtain the benefits from cooperating in providing basic medical services. For public sectors, it is their responsibility to provide basic medical services. The private sectors can solve financial shortages and share part of the risk with public sectors. For the private sector, entering the medical field as the basic public service allows it to obtain research data, public equipment resources, and promote the development of related research, hence greatly enhancing the value of their company. It is a positive verification of our model.
“瑞金模型”是中国医改中非常重要的一步，也是验证我们矩阵数学模型计算的案例 。 自 2013 年原卫生部部长陈竹在全国卫生大会上提出以来，全国 MA 越来越多，管理和合作模式多种多样。其中最成功的案例之一是“瑞金模式”。2016 年 3 月 16 日，上海交通大学医学院瑞金医院（瑞金医院简报）联合上海其他 8 家医院，联合成立“瑞金血液学硕士”，这是上海市首家血液学硕士。整合共享医疗资源，解决血液病患者的实际问题。 十年前，也是瑞金医院创办了上海市第一个医联会（马萨诸塞州卢湾区）。在本次 MA 中，公营部门和私营部门都可以从合作提供基本医疗服务中获得好处。对于公共部门来说，提供基本医疗服务是他们的责任。私营部门可以解决财政短缺问题，并与公共部门分担部分风险。对于民间来说，进入医疗领域作为基础公共服务，可以获取研究数据、公共设备资源，促进相关研究的发展，从而大大提升其公司的价值。 这是对我们模型的积极验证。
However, things have changed over the years.One reason why private capital maintains a high enthusiasm for participating in the construction of non-profit hospitals is that in the joint construction of PPP hospitals, the hospital's supply chain can be a subsidiary or affiliated enterprise of the investor. Private capital indirectly shares the hospital's profits by improving procurement efficiency and reducing costs through the income from the supply chain. As private sector becomes unprofitable, the failure of joint construction of multiple PPP hospitals in recent years has indeed diminished the enthusiasm of private capital.
然而， 多年来，情况发生了变化 。 民间资本之所以对参与非营利性医院建设保持着高涨的热情，一个原因是在 PPP 医院的联合建设中，医院的供应链可以是投资方的子公司或关联企业。民间资本通过供应链收入，通过提高采购效率、降低成本，间接分享医院利润。 随着民间变得无利可图，近年来多家 PPP 医院联合建设的失败，确实削弱了民间资本的积极性。
China Health Group (00673), listed on the Hong Kong Stock Exchange, is a Hong Kong investment holding company primarily engaged in the buying and selling of medical equipment and consumables. The company operates through four major divisions. The branch of buying and selling medical equipment and consumables operates the business of buying and selling medical equipment and trading medical consumables; The hospital management business division operates and manages Shuangluan Hospital, Anping Boai Hospital, Luanping County Red Cross Hospital, and Luanping County Hongfu Nursing Home, among others; The property investment division acquired the property of Anping Boai Hospital, bringing in rental income; The commercial factoring business division operates hospital commercial factoring business.The company has gathered a team of hospital directors with excellent medical skills and rich experience. Through an information platform, years of hospital management experience are presented in a standardized and digitized manner, managed through systems rather than human intervention, effectively improving management efficiency. Thanks to scientific treatment, the scale and revenue of hospitals managed or operated by the company have significantly increased. It is reported as a star PPP project for a time.Due to changes in national policies, the original agreement cannot continue to be fulfilled. After friendly negotiations, on April 30, 2021, China Health Group and the district government signed a termination agreement. According to the termination agreement, the district government should return the loan principal to China Health Group and calculate interest at an annual rate of 7%. However, after the signing of the termination agreement, the district government has been unable to fulfill its repayment obligations as agreed. After multiple reminders from China Health Group, on June 21, 2022, the district government issued a "Commitment Letter" confirming and agreeing to repay the outstanding balance of RMB 47.158 million owed by China Health Group. In the commitment letter, the district government also issued a repayment plan: repay RMB 500000 by the end of June 2022, RMB 1 million by the end of July 2022, RMB 2.5 million by the end of August 2022, and RMB 43.158 million by the end of September 2022. China Health Group acknowledges this. Subsequently, in June 2022, the district government repaid RMB 500000 to the company. Failure to continue repayment according to the repayment plan thereafter. Since June 2022, China Health Group has sent multiple reminders to the district government, and later sent someone to negotiate repayment matters with the district government in May 2024. The district government fully confirms its repayment obligation and voluntarily expresses its willingness to repay, and has conducted specific negotiations with all parties on the repayment method. In July 2024, the district government repaid RMB 200000 to the company. As of the date of the complaint, the district government has not been able to repay all outstanding debts. Now, China Health Group has filed a lawsuit, requesting that the district government and district people's hospital jointly repay the principal debt of RMB 50.9868 million to China Health Group in accordance with the law, and pay interest to China Health Group, totaling RMB 59.0774 million. It is also a verification of our model.
中国健康集团（00673），于香港联交所上市，是一家主要从事医疗设备及耗材买卖的香港投资控股公司。该公司通过四个主要部门运营。医疗器械耗材买卖分公司经营医疗器械买卖及医用耗材交易业务;医院管理事业部运营管理双滦医院、安平博爱医院、滦平县红十字会医院、滦平县宏福养老院等;物业投资事业部收购安平博爱医院物业，带来租金收入;商业保理业务部经营医院商业保理业务。公司聚集了一支医术过硬、经验丰富的医院院长团队。通过信息平台，将多年的医院管理经验以标准化、数字化的方式呈现，通过系统管理，而不是人为干预，有效提高管理效率。得益于科学治疗，公司管理或运营的医院规模和收入均有明显增长。一度被报道为明星 PPP 项目 。由于国家政策的变化，原协议无法继续履行。经过友好协商，2021 年 4 月 30 日，中国健康集团与区政府签署了终止协议。根据终止协议，区政府应将贷款本金返还给中国健康集团，并按年利率 7%计算利息。 然而，在终止协议签署后，区政府一直无法按约定履行还款义务。经中国健康集团多次提醒，2022年6月21日，区政府出具《承诺函》，确认同意偿还中国健康集团欠款4715.8万元。在承诺书中，区政府还出台了还款预案：2022年6月底前还款50万元，2022年7月底前还款100万元，2022年8月底前还款250万元，2022年9月底前还款4315.8万元。中国健康集团对此表示认可。随后，2022年6月，区政府向公司偿还了50万元人民币。此后未能按照还款计划继续还款。自2022年6月以来，中国健康集团多次向区政府发出催款，后于2024年5月派人与区政府协商还款事宜。区政府充分确认还款义务并自愿表示还款意愿，并已就还款方式与各方进行了具体协商。2024年7月，区政府向公司偿还人民币20万元。截至投诉之日，区政府尚未能够偿还所有未偿债务。现在，中国健康集团已提起诉讼，要求区政府、区人民医院依法共同偿还中国健康集团本金5098.68万元，并向中国健康集团支付利息，共计5907.74万元。这也是对我们模型的验证。
The significance of the matrix mathematical model
矩阵数学模型的意义
PPP model in the field of health has lots of issues.(16) (17) (18) In the further direction of Chinese MA, PPP model could still be an alternative (14). Basically, according to our matrix mathematical model, the sustainable development of MA in the PPP model must take into account the dynamic interactions of five parties: the government, the medical insurance organizations, the public hospitals, the private sectors and the patients (19), especially on the topic of assessing PPP in Chinese healthcare (20). The ideal model of MA in PPP model should benefit the public hospital, the private sector and the patients without increasing the cost of basic medical services. Basic medical services are an important part of the government's public service, and its reform involves all aspects, from the construction of non-profit medical institutions to the provision of basic medical services. Thus, MA in China can choose different PPP models depending on different situations. At present, the PPP model mainly includes outsourcing, franchising, and privatization.
卫生领域的 PPP 模式存在很多问题 。（16）（17）（18） 在中国语的进一步发展方向上，PPP 模式仍可作为替代方案 （14）。 基本上， 根据我们的矩阵数学模型，PPP 模型中 MA 的可持续发展必须考虑政府、医保组织、公立医院、私营部门和患者五方的动态相互作用 （19）， 特别是在评估中国医疗保健中的 PPP 这一话题（20）。PPP 模式中理想的 MA 模式应在不增加基本医疗服务成本的情况下惠及公立医院、私营部门和患者。基础医疗服务是政府公共服务的重要组成部分，其改革涉及到从非营利性医疗机构的建设到提供基本医疗服务的各个方面。因此，中国的 MA 可以根据不同的情况选择不同的 PPP 模式。目前，PPP 模式主要包括外包、特许经营、私有化等。
Most of the Chinese hospitals in Chinese Mainland are non-profit medical institutions. In terms of non-profit medical institutions, China stipulates that the profit a public hospital makes cannot be distributed to shareholders and can only be used for the construction and reinvestment of hospitals. For those private sectors in MA, the model of franchising PPP is very useful to understand the profit distribution for their shareholders. For example, in the agreement of MA between the public side and the private sectors: the private medical groups annually invest a fixed fund to the MA in exchange for the right to manage MA for a specific period, and get the right to collect management fees based on its management performance. It also has the right to provide medicines, medical devices and medical consumables to the public hospital in agreement of the MA. When the agreement expires, the private sector transfers management rights to the owner of MA. This agreement belongs to a typical franchise mode, and the investment obligation of private sectors can also be regarded as privatization in a broad sense. “Privatization” cooperation should generally cooperate with franchising; otherwise it is difficult to guarantee the profit making of private sector.It is very difficult to do this in Chinese Mainland actually.
中国大陆的华人医院大多是非营利性医疗机构。在非营利性医疗机构方面，中国规定公立医院赚取的利润不能分配给股东，只能用于医院的建设和再投资。对于马萨诸塞州的私营部门来说，特许经营 PPP 模式对于了解其股东的利润分配非常有用。例如，在公私部门的 MA 协议中：民营医疗集团每年向 MA 投入固定资金，以换取一定时期的 MA 管理权，并根据其管理绩效获得收取管理费的权利。它也有权在金融管理专员的协议下向公立医院提供药物、医疗器械和医疗消耗品。协议到期后，私营部门将管理权转让给 MA 所有者。该协议属于典型的特许经营模式，民间的投资义务也可以看作是广义的私有化。“私有化”合作一般应配合特许经营;否则，很难保证私营部门的盈利。实际上，在中国大陆很难做到这一点。
The current MA in PPP model covers diverse ways of cooperation. Those deepening in cooperation may also contain multiple modes of an MA project. The wide application of MA in PPP model should not be divided into the simple pattern, but should be specific in detailing content according to the implementation method, especially in Chinese health care.
目前的 MA 在 PPP 模式涵盖了多种合作方式。深化合作的项目也可能包含 MA 项目的多种模式。MA 在 PPP 模式中的广泛应用不应分为简单的模式，而应根据实施方法具体细化内容，尤其是在中国医疗保健领域。
In order to ensure the state-owned property in Chinese health care, MA infrastructure construction and renovation can be regarded as the city infrastructure construction. Using the franchise model as a wide application of practice, it maximizes the use of social capital, and completes the MA construction with high quality. To ensure the private sector in MA makes profits, the government can pay management fees to the private sector yearly.
为了保证中国医疗卫生的国有财产，马州基础设施建设改造可以看作是城市基础设施建设。以特许经营模式作为实践的广泛应用，最大限度地利用社会资本，高质量完成 MA 建设。为确保马萨诸塞州的私营部门盈利，政府可以每年向私营部门支付管理费。
In addition, the non-profit Chinese hospital in MA, because of its public welfare, has had loan difficulties from the bank (usually the public sector in MA uses credit loan in application of the bank loan). With the application of MA in Chinese hospital, PPP model will be of importance in small cities. An outsourcing way of outsourcing the PPP model can be adopted. The private sector can take part in the core medical services together with the Referral system used by the Chinese government.
此外，马萨诸塞州的非营利性华人医院，因为公益性问题，也出现了银行贷款困难（通常马萨诸塞州公共部门在申请银行贷款时使用信用贷款）。随着 MA 在中国医院的应用，PPP 模式在小城市中将具有重要意义。可以采用 PPP 模式的外包方式。私营部门可以参与核心医疗服务以及中国政府使用的转诊系统。
For the selection of the private sectors in MA, “money” should not be the only selection standard. Financial capacity, professional background, organization, coordination abilities should also be taken into consideration. In addition, an effective system of accountability should be established on the basis of long-term agreements and contracts, so as to ensure the realization of cooperation to the maximum extent. In accordance with modern corporate structures to strengthen the internal management of MA, proper application of mixed stock ownership system in MA can stimulate the Chinese hospitals, and constantly improve the level and efficiency of Chinese health care.
对于马萨诸塞州私营部门的选择，“钱”不应成为唯一的选择标准。还应考虑财务能力、专业背景、组织、协调能力。此外，还应该在长期协议和合同的基础上建立有效的问责制度，以最大限度地保证合作的实现。按照现代公司结构加强 MA 内部管理，合理应用混合股制，可以刺激中国医院的发展，不断提高中国医疗卫生的水平和效率。
Conclusion
结论
As an important measure of China’s new medical reform, MA is still now in the immature stage. Multi-sector collaborative reform is underway.Although PPP model in the field of health has lots of issues, it could still be a way of realizing Medical Alliance in Chinese medical service(Fig 2). We conduct a matrix mathematical model and suggest ways that could be used in those MAs to achieve their expected goal and mutually benefit in both the public and private sectors.
作为中国新医改的重要举措，MA 目前仍处于不成熟阶段。多部门协作改革正在进行中。 尽管 PPP 模式在健康领域存在诸多问题 ， 但仍可成为实现中国医疗服务医学联盟的一种方式 （图 2）。 我们进行了矩阵数学模型，并提出了可用于这些 MA 的方法，以实现其预期目标并在公共和私营部门互惠互利。
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