Table 3 Design and explanation of the SD equation

(1) Institutional performance = INTEG (Institutional input + Service output + Institutional satisfaction)

Institutional performance consists of Institutional input, Service output, and Institutional satisfaction. The initial value is set to 1

(2) Institutional input = 0.1* Information system resource investment + 0.5* Element input + 0.2* Capital investment

The weights of the three components of Institutional input are slightly different in the literature. This paper takes the average value of the research results of various scholars

(3) Human Investment = Administrative staff + (Medical staff + Elderly care workers)* Service personnel professionalism

The professional degree of service personnel who directly serve the elderly has a great impact on the level of human resources in institutions

(4) Institutional operating investment = STEP(0.1* Institutional profitability, 36) + 0.5

The initial operating investment of the institution is 0.5, and 10% of the institutional profit begin to be the main investment after three years

(5) Local financial subsidies = Policy support *PULSE TRAIN(12,1,12,120)

Government subsidies to institutions have a time interval, generally once a year

(6) Information system resources = (0.3* Information sharing system + 0.3* Health monitoring equipment)* Internet usage level

The Internet usage level has a positive impact on the use of institutional hardware and software

(7) Service output = (Service capability + Service level + Service sustainability)* Input conversion rate

Considering the depreciation and the turnover, the resource input of the institution cannot be fully transformed into the output of the institution

(8) Input conversion rate = 0.8

It is assumed that 80% of institutional input can be transformed into institutional service output

(9) Service capability = Service content * Service quality

Service capability is affected by service content and service quality

(10) Service quality = SMOOTH(Policy support,60,0.1)* Maturity of medical-elderly care integrated institutions

The role of quality norms is not achieved overnight. It is assumed that the 60th month after the release of the policy can fully play the role of quality assurance

(11) Service sustainability = (Institutional social recognition + Financial Status of the Institution)/ Turnover rate of service staff

The social recognition and financial status of institutions have a positive impact on service sustainability, while the turnover rate has a negative impact

(12) Institutional satisfaction = 0.35* Social recognition of institutions + 0.65* Satisfaction of the relevant personnel

The weight setting method is the same as the Institutional input

(13) Elderly satisfaction = Service level / Service complaint rate

Elderly satisfaction is positively correlated with service level and negatively correlated with service complaint rate

(14) Service complaint rate = 1/ Service quality

The service complaint rate is negatively correlated with service quality

(15) Family and guardian satisfaction = DELAY1(Elderly satisfaction,2)

The evaluation of the institution by the family members directly comes from the elderly, but there is a time difference. The satisfaction of the elderly will affect the family members after two months

(16) Internet usage level = Internet usage level table(Time)

The change of Internet usage level over time is nonlinear, so the model uses a table function

(17) Internet usage level table = [(0,0.7)- (130,0.8)],(0,0.7),(10,0.73),(20,0.76), (30,0.773),(40,0.781),(50,0.785), (60,0.788),(70,0.789),(80,0.79), (90,0.791),(100,0.792),(110,0.793), (120,0.794)

From LJ [52]: Prediction of Internet penetration in China based on innovation diffusion theory