Chronic disease management has always been the focus and a difficult domain of health management in China (1). According to the statistical data from WHO (https://ncdportal.org), 74% of world deaths are caused by non-communicable diseases (NCD), among which 4 categories of chronic diseases named cardiovascular and cerebrovascular diseases (i.e., heart disease and stroke, including hypertension), cancer, chronic respiratory diseases, and diabetes are the top 4 prevalent diseases having caused 15.8, 8.4, 3.6, and 1.7 million deaths, respectively in the year 2019. In China, the proportion of chronic disease causing deaths in the total number of deaths is as high as 86.6%, and the burden caused by it has accounted for more than 70% of the total disease burden. The official statistical results of the National Health Commission of the People's Republic of China (http://www.nhc.gov.cn) show that in 2021, the medical expenditure for chronic diseases in China rose to about 4,679.8 billion, and as the top 1 killing disease and the most typical chronic disease, more than 300 million people are suffering from cardiovascular and cerebrovascular diseases in China. In 2019, the total hospitalization expenses of cardiovascular and cerebrovascular diseases in China were 313.366 billion CNY (2, 3). Chronic diseases lead to frequent doctor–patient communication and prescription, i.e., “re-visits and drug renewal,” which require a large amount of medical resources. During the COVID-19 pandemic, a large number of medical resources were allocated to the anti-pandemic campaign, and people's travel was greatly restricted (4), which made the review of chronic disease patients and drug renewal significantly difficult. Therefore, it is a feasible way for chronic disease patients to be diagnosed and treated at home with the help of online diagnosis and treatment services and intelligent medical devices. Due to COVID-19, countries around the world began to vigorously promote online diagnosis and treatment services, such as the Chinese “14th Five-Year Plan” published in 2021 (5), the American Omnibus Appropriations Act of 2021 (6), and the American Rescue Plan Act of 2021 (7) to continue and expand telehealth funds and reimbursement. Then, the development of online medical services is reinforced by more and more national strategies all over the world (8, 9).

Internet hospitals, are online healthcare platforms operated by physical medical institutions which can be categorized into 2 modes: self-built (built as a standalone system by physical medical institutions themselves) and relying on (built on the third-party Internet platforms) (10). As of March 2022, there were more than 1,700 of them in China (data source: 2022 National Committee of the Chinese People's Political Consultative Conference). A key business of Internet hospitals is “re-visits and drug renewal” (11), and they help to overcome the constraints of pandemic situations and the shortages of physical medical resources in underdeveloped areas (12). In addition to Internet hospitals, chronic disease patients can enjoy online diagnosis and treatment services through medical service platforms, such as Good Doctor Online, WeDoctor, Ping An Good Doctor in China, and Amwell and BetterHelp in the U.S.A., most of whom are not equipped for physical diagnosis (13). They employ full-time doctors (such as Ping An Good Doctor) or part-time doctors (such as Good Doctor Online) (14) with the mode of “family doctor, multi-site practice” gradually accepted by patients, doctors, and hospitals (15).

Whether chronic disease patients are willing to choose online diagnosis and treatment services is still an interesting topic under research. Li and Qiu believe that if telehealth can satisfy or exceed the doctor-patient interaction level of the traditional medical treatment process, patients will turn to choose online diagnosis and treatment services (16, 17). Also, doctors' response time of the first-visit has a significant impact on the re-visits behavior of the patients (18–22). Additionally, patients should change their habits and utilize online diagnosis and treatment resources for health management (23) and a proactive chronic disease health management mode is worth popularizing (24). So, it is necessary for chronic disease patients to form the habit of utilizing online diagnosis and treatment services during the pandemic.

The demand for medical devices is frequent and even continuous for chronic disease patients, accompanied by big data and artificial intelligence are increasingly empowering the medical device and health industry (25). Wearable technology has played an essential role in Mobile Health (26), which helps to detect and monitor the physiological status of patients anytime and anywhere and can process collected data intelligently, thus providing data support for online diagnosis and treatment (27, 28). For example, a wearable body condition sensor system can wirelessly monitor one's sleep posture and breathing rate and timely feedback to the nursing staff of vulnerable groups (29), and Bittium HolterPlus can conduct daily data checks and ECG analyses to provide information for doctors' diagnoses. More and more such medium- and high-value durable medical devices will be obtained by leasing besides selling under the global sharing economy trend. So besides going to hospitals, chronic disease patients can carry out health management processes such as “re-visits and drug renewal” at home with the help of online diagnosis and treatment services and intelligent medical devices.

According to the exploration of the chronic disease diagnosis and treatment system, four main stakeholders including physical medical institutions, medical service platforms (online appearing as website, APP, WeChat official account, Wechat Mini Program et al. and conducted by online medical service organizations), intelligent medical device providers, and chronic disease patients are recognized, whose strategy choices affect each other and all of whom expect to get maximum benefit. Chronic disease patients may choose traditional offline (on-spot) diagnosis and treatment services, or novel online diagnosis and treatment services through three channels (i.e., “self-built” mode Internet hospitals, “relying on” mode Internet hospitals, and medical service platforms). “Relying on” mode Internet hospitals have their advantages over the counterpart one “self-built” in development, maintenance costs, and patient acquisition due to economy of scale, while it is vice versa in sensitive data security. Medical service platforms have a competitive relationship with physical medical institutions on patients. Medical service platforms can employ part-time doctors engaged in multi-site practice to work on the platforms or recruit full-time doctors. Part-time wages will be lower than full-time wages and part-time doctors are important resources (30, 31). The part-time doctor mode has low costs and low response speeds, while the full-time doctor mode has high costs but high response speeds. Whether intelligent medical device providers lease devices will affect the health management cost of chronic disease patients. As an increasing number of chronic disease patients use intelligent medical devices, this will reduce the frequency of patients going to physical medical institutions, indirectly affecting the preference of chronic disease patients, and thus affecting the strategic choices of the other two stakeholders.

This paper aims to describe and solve the following three problems:

Evolutionary game theory is a powerful tool and can help to explore these problems. It assumes that all participants are bounded rational, constantly adjusting their strategies according to the payoff situation in the game's process, and seek equilibrium through the dynamic process of multiple games, so it is widely used to study and discuss the behavior of interest groups (32). Chen et al. constructed an evolutionary game model of hospitals and patients to analyze the current situation of telehealth in China (33). Yuan et al. constructed a bilateral GNPO-hospital game model in the Chinese context and discussed the strategies and influencing factors of medical supply allocation in public health emergencies based on evolutionary game theory (34). With the evolutionary game model, Xu et al. analyzed the stable evolutionary strategies between the urban and rural medical and health facilities (35). Fei et al. constructed a tripartite evolutionary game model of medical insurance fraud and studied the formation mechanism of medical insurance fraud (36). Gao et al. studied a tripartite evolutionary game of cross-regional hospitals and patients' choice behavior in telehealth, in which an important factor affecting the telehealth system was the operating cost of general hospitals (37). Zhu et al. constructed a tripartite evolutionary game model for system providers, hospitals, and governments to analyze privacy problems under mobile medical care, in which strategic choices of medical health system providers and hospitals are relevant to profits and investment costs (38). Liu et al. constructed an evolutionary game model to explore the relationship between the government and family medical care, and studied the recycling of wasted household medical devices (39). Xiao et al. established a tripartite evolution model of government, hospitals, and enterprises and noted that the main reason influencing consumers' choice of new medical products was product income (40). Yu et al. constructed a tripartite evolutionary game for higher medical institutions and primary medical institutions, and found that when the benefit outweighs the costs, higher medical institutions, primary medical institutions, and patients will actively promote the benign interaction of telemedicine (41).

The existing evolutionary game literature analyzed the current situation of telemedicine and various problems under the background of telemedicine by constructing evolutionary game models for hospitals and patients or system providers, considering factors such as those affecting the development of telemedicine systems and privacy issues under mobile medicine. On this basis, this paper examines the problem of “re-visits and drug renewal” in the post-pandemic era for chronic disease patients in the context of telemedicine and by means of the evolutionary game model. The model consists of four main stakeholders: physical medical institutions that carry out online and offline diagnosis and treatment services, medical service platforms that carry out online diagnosis and treatment services, intelligent medical device providers that provide intelligent medical devices for chronic disease patients, and chronic disease patients receiving diagnosis and treatment services. The interaction of the four groups of subjects will directly affect the development trend of the systems. The model was constructed according to the cost parameters, benefit parameters, and other parameters of the stakeholders under different circumstances. According to the strategic stability points (ESSs) obtained by evolutionary game analysis, we determined the key factors affecting the choice of the stakeholders and proposed governance mechanisms of chronic disease diagnosis and treatment systems.

This paper will take cardiovascular and cerebrovascular diseases as an example of chronic diseases to build the evolutionary game model. Cardiovascular and cerebrovascular patients are high-risk groups during the pandemic, and easy to induce severe illnesses once occur, so it is particularly necessary to implement health management processes with the help of online diagnosis and treatment services and intelligent medical devices during the pandemic. Cardiovascular and cerebrovascular patients can buy or lease cardiovascular and cerebrovascular therapeutic devices and other medical devices to test their physical indicators at home and follow up offline or online “re-visits and drug renewal.” In addition to traditional offline diagnosis and treatment, physical medical institutions will still perform online diagnosis and treatment. Physical medical institutions can establish online healthcare platforms by themselves or choose to rely on third-party Internet platforms, so their strategy set is denoted as {self-built, relying on}. Medical service platforms can employ part-time doctors or full-time doctors, so their game strategy set is denoted as {part-time doctors, full-time doctors}. Chronic disease patients tend to evaluate the strength, reputation, and experience and choose to go to specific physical medical institutions for offline diagnosis and treatment (42, 43). While chronic disease patients who prefer online diagnosis and treatment have the preference for the Internet. So their strategy set is denoted as {physical preference, Internet preference}. Intelligent medical device providers can choose whether to provide device leasing, so their strategy set is denoted as {leasing, no leasing}. Intelligent medical devices were used to detect health indicators of chronic disease patients, and online or offline visits were selected according to preferences to implement the process of “re-visits and drug renewal.”

The study made the following assumptions and had the following parameter settings:

The variables and proportions of stakeholders choosing different strategies are shown in Table 1. The evolutionary game payoff matrix is shown in Table 2, then the expected payoffs and replicator dynamic equations of each stakeholder group can be figured out according to the regulation of evolutionary game theory (37–40).

Consider that the proportion of physical medical institutions that choose the “self-built” strategy is x; then, the proportion that choose the “relying on” strategy is 1 − x. The expected payoff of the two physical medical institution sub-groups are U_1x, U_2x, respectively. The expected total mean payoff is Ux¯, then,

Calculating replicator dynamic equations is a common step in evolutionary game analysis (37–40). According to the expected payoff expressions of physical medical institutions, the replicator dynamic equation of physical medical institutions is:

The proportion of platforms that choose the “part-time doctor” strategy is y; then, the proportion that choose the “full-time doctor” strategy is 1 − y. The expected payoff of the two medical service platform sub-groups are U_1y, U_2y, respectively. The expected total mean payoff is Uy¯, then,

The replicator dynamic equation of medical service platforms is:

Besides sale, the proportion of the intelligent medical devices providers that choose the “leasing” strategy is z; then, the proportion that choose the “no leasing” strategy is 1 − z. The expected payoff of the two provider sub-groups are U_1z, U_2z, respectively. The expected total mean payoff is Uz¯, then,

The replicator dynamic equation of intelligent medical device providers is:

The proportion of chronic disease patients who choose the “physical preference” strategy and adhere to the traditional offline physical medical institutions is p; then, the proportion of those who choose the “Internet preference” strategy is 1 − p. The expected payoff of the two patient sub-groups are U_1p, U_2p, respectively. The expected total mean payoff Up¯, then,

The replicator dynamic equation of chronic disease patients is:

The evolutionary game of the chronic disease diagnosis and treatment system is an asymmetric multi-group game. Selten et al. affirmed that the asymptotically stable solution of a replicator dynamic system in a multi-group evolutionary game must be a strict Nash equilibrium solution, and the evolutionary stable strategy (ESS) of a multi-group evolutionary game must be a pure-strategy Nash equilibrium (45). The asymptotic stability of the potential equilibrium points corresponding to each pure strategy combination can be judged by the Lyapunov first method. If and only if all the eigenvalues of the Jacobian matrix corresponding to the potential equilibrium point are negative, the equilibrium point is ESS. The analysis results are shown in Table 3.

By analyzing the eigenvalue expressions in Table 3, it was found that there were mutual exclusion constraints on the eigenvalues of different potential equilibrium points. If a point satisfies the condition of stability, the potential equilibrium point with mutual exclusion constraints cannot be stable. Based on this, the compatibility among conditions 1–10 are shown in Table 4.

It can be seen from Table 4 that if Condition 1 is satisfied, that is, the strategy corresponding to Condition 1 is ESS, the ESS corresponding to Conditions 2, 3, 4, 6, 7, 8, and 10 cannot be ESS, but one of Condition 5 or Condition 9 may be satisfied, that is, the final evolution results are two ESSs. Similarly, if Condition 2, 4, or 7 is satisfied, Condition 5 or Condition 9 may also be satisfied. It can also be obtained from Table 4 that only a unique ESS exists when Condition 3, 6, 8, or 10 is satisfied. To show the evolution process and the results of the chronic disease diagnosis and treatment replicator dynamic system more intuitively, a simulation analysis is performed using the Matlab2021 software. The initial values of the variables were in accordance with the magnitude relationship of the values detailed in the 2nd section with the support of literature (16–20, 30, 44) and withdrawn from dozens of visits of cardiovascular and cerebrovascular patients, hospitals, medical service platforms, and intelligent medical device providers. The parameters initiation is shown in Table 5.

From the forgoing analysis, it can be concluded that there are 10 possible equilibrium stable points (ESSs) in the chronic disease diagnosis and treatment systems, and which one is the ultimate ESS determined by the initial conditions. The optimal strategies obtained from Analysis of optimal strategies and influencing factors section are (0, 1, 1, 0) and (1, 1, 1, 0). Meanwhile, we obtained their intrinsic mechanisms by evolutionary game analysis and simulation. The net benefit of different strategies affects the strategy choice of each game player, and the magnitude of expressions shown in Table 4, will affect the speed of evolution. Therefore, mechanisms can be designed to make the situation meet condition 6 or condition 10 to guide all players to evolve toward their optimal strategy.

This evolutionary game model only considered four stakeholder groups, and was constructed wholly based on endogenous variables since the exogenous variables related to other groups including the government and third-party platforms were internalized, such as exogenous variables of government subsidies and tax break have been internalized into the revenue related endogenous variable of “benefit.” When designing the governance mechanisms, we can unfold reversely and link the endogenous variables to the behaviors of these other groups. As a special external coordinator having an important impact on the chronic disease diagnosis and treatment systems, the government here is highlighted and introduced as a key participant in the following governance mechanisms design. In addition to the efforts of the four stakeholder groups themselves, the government can play a very important role when needed. Related researches show that government tools including subsidies and tax policies can guide the behaviors of social entities such as innovation (51–53).

During the pandemic, strict supervision is performed all over the country for the safety of the public in China, and never slack even during the current post-pandemic era. It is difficult for chronic disease patients to do “re-visits and drug renewal” (4). By analyzing the construction modes of online healthcare platforms (10) and the development of online diagnosis and treatment (11–13), it was found that online diagnosis and treatment services play an important role in solving the problem of offline “re-visits and drug renewal” for chronic disease patients (14). By increasing the willingness of chronic disease patients to see a doctor on the Internet, chronic disease patients can turn to enjoy online diagnosis and treatment services (16, 17). Additionally, due to the development of science and technology, intelligent medical devices can help chronic disease patients better carry out online “re-visits and drug renewal.” Chronic disease patients can use intelligent medical devices to detect or monitor their physiological indicators anytime and anywhere, providing data for online diagnosis and treatment (25, 26). Therefore, the combination of online diagnosis and treatment services along with intelligent medical devices plays a very important role in the “re-visits and drug renewal” of chronic disease patients and their chronic disease management. Chronic disease patients use intelligent medical devices to detect health indicators and choose online or offline visits to complete the process of “re-visits and drug renewal” according to their preferences. This model is worth popularizing (24). In this paper, four stakeholders named physical medical institutions, medical service platforms, intelligent medical device providers, and chronic disease patients, were linked to form a chronic disease diagnosis and treatment system to study chronic disease patients' “re-visits and drug renewal” problem using the method of evolutionary game theory.

In other evolutionary game models used to explore the relationship between hospitals and patients or system providers in the context of telemedicine, it was found that the operating costs of general hospitals are an important factor affecting telemedicine systems (37), and the strategic choices of system providers and hospitals are relevant to profits and investment costs (38). When the benefit of medical institutions and patients outweigh the costs (41), they will actively promote the benign interaction of telemedicine. On this basis, in this paper, the problem of chronic disease patients' “re-visits and drug renewal” in the context of telemedicine was studied, and the cost and benefit parameters were set to study the chronic disease diagnosis and treatment system; additionally, the different costs and benefit of medical service platforms due to the different response speeds of full-time doctors and part-time doctors were taken into account. In the research on medical device recycling (39, 40), it was found that there is a great demand for household medical devices. The market potential is huge. Moreover, the relevant government measures will improve the probability that enterprises choose to recycle. Therefore, we took into account intelligent medical device providers who provide intelligent medical devices for chronic disease patients in the process of “re-visits and drug renewal” and their health management and studied the impact of whether intelligent medical device providers choose to lease or not on the chronic disease diagnosis and treatment system.

In this study, we constructed an evolutionary game model of diagnosis and treatment systems for chronic diseases. We have discussed the mutual influence between physical medical institutions providing online and offline diagnosis and treatment, medical service platforms providing online diagnosis and treatment, intelligent medical device providers providing intelligent medical devices, and chronic disease patients. The evolutionary game payoff matrix was constructed, and the Jacobian matrix of the system was obtained by calculating replicator dynamic equations. According to the Lyapunov's first method that if the eigenvalues are <0, the possible stable points of the system are judged. It can be seen from Table 3 that there are 10 evolutionary stability strategies (ESSs) in the system. From Table 4, we can see the conditions under which 10 evolutionary stability strategies (ESSs) are confirmed. MATLAB2021 is used for data simulation, and it can be seen that when different initial conditions are satisfied, 10 possible stable points hold, respectively. Using the evolutionary game method, we explored how each stakeholder in chronic disease diagnosis and treatment systems makes strategic choices, determined the key factors affecting each stakeholder's choice, summarized the intrinsic operating mechanism of chronic disease diagnosis and treatment systems and obtained two optimal evolutionary stability strategies (ESSs) through optimal strategies and influencing factors analysis sections. Because the evolution direction of the system is relevant to the initial status of the system, the initial conditions can be adjusted by governance mechanisms designed to better coordinate the four stakeholders to make more favorable choices and to provide guidance and reference for the improvement of chronic disease diagnosis and treatment systems. The simulation in this study had a close relationship with the initial probabilities of the first strategy of the four stakeholders. It showed that when the relevant policies change and adjust, the simulation will have different trends. In the case of flexible policies, different models need to be established for further research. In addition, we did not consider the impact of the environment or the reference price effect (56), which will also be the focus of our future research.

To solve the difficulty of “re-visits and drug renewal” for chronic disease patients during the COVID-19 post-pandemic era, this paper puts forward a diagnosis and treatment pattern combining online diagnosis and treatment with intelligent medical devices, discusses its possibility, and designs governance mechanisms to promote the development of the diagnosis and treatment systems for chronic diseases toward the desired direction. We constructed an evolutionary game model of chronic disease diagnosis and treatment systems from the perspective of stakeholders. Using evolutionary game analysis, we studied how physical medical institutions, medical service platforms, intelligent medical device providers, and chronic disease patients make their choices under different circumstances, and the replicator dynamic equations of different groups were obtained. Through our analysis, two optimal evolutionary stable strategies, (0, 1, 1, 0) and (1, 1, 1, 0), were obtained; a simulation analysis was carried out; we summarized the intrinsic operating mechanisms of chronic disease diagnosis and treatment systems, and the following conclusions can be drawn:

Conclusion 1: Available from Table 4 and Section Cases with two ESSs at the same time, in the cases of two ESSs at the same time, the evolution direction is relevant to the initial probability. The preference of chronic disease patients is relevant to the initial probability. When the probability rises to > 0.5, chronic disease patients will change from an Internet preference to a physical preference. When chronic disease patients prefer physical institutions, physical medical institutions and medical service platforms will choose low-cost strategies, that is, physical medical institutions will choose the “relying on” mode, while medical service platforms will choose the “part-time doctors” mode.

Conclusion 2: Available from Table 4 and Section Cases with unique ESS, the net benefit affects the strategic choice of the four groups of stakeholders. By adjusting the benefit, the evolution direction can be changed. In the cases of only one ESS, chronic disease patients have an Internet preference. When chronic disease patients prefer the Internet, physical medical institutions, medical service platforms, and intelligent medical device providers will choose the strategy with the larger net benefit.

Conclusion 3: According to the sensitivity analysis involved in section Analysis of optimal strategies and influencing factors, the evolution speed of chronic disease diagnosis and treatment service systems can be changed. Increasing the difference in expression leading to changes of the corresponding expression can accelerate the evolution, that is to say, changing the key factors can affect the evolution speed of chronic disease diagnosis and treatment systems.

Finally, by combining the evolutionary game model analysis and the simulation results, two optimal evolutionary stability strategies (ESSs) were taken as guidance. Four governance mechanisms were proposed, including the Internet preference guidance mechanism for chronic disease patients, the online diagnosis and treatment supporting mechanism, the incentive mechanism for doctors by medical service platforms, and the supporting mechanism for intelligent medical device providers. Under the function of the governance mechanisms, expressions' values in Table 4 can be changed, then chronic disease diagnosis and treatment systems can evolve toward the desired direction. That is to say, physical medical institutions choose either “self-built” mode or “relying on” mode, is according to their net benefit; medical service platforms adopt the “part-time doctor” mode; intelligent medical device providers adopt the “leasing” mode; chronic disease patients prefer the Internet. Looking ahead, it is highly recommended that physical medical institutions choose “relying on” mode and rely on the IT services provided by the medical service platforms. Therefore, this provides guidance and acts as a reference for stakeholders to better promote the improvement of chronic disease diagnosis and treatment systems.

Code Availability: Model calculation and simulation figures production is produced by MATLAB2021 software. Specific operating instructions can be found at: https://github.com/qduzl/wxf. Inquiries can be directed to the corresponding authors to obtain code files for simulation.

LZ, XW, XL, and YL: conceptualization. LZ, XW, and HX: methodology and writing—original draft preparation. XW, GD, YS, and YD: investigation. XW: software and visualization. XW and LZ: formal analysis. XL, YS, and YD: data curation. CM, GD, and YD: validation. XW, HX, LZ, CM, YD, and YL: writing—review and editing. XW and HX: supervision. LZ: funding acquisition. All authors contributed to the article and approved the submitted version.